text
stringlengths 209
2.82k
| label
int64 0
1
|
|---|---|
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces generalized Raynaud surfaces; surfaces of general type; global vector fields; characteristic p W. Lang, ``Examples of surfaces of general type with vector fields'' in Arithmetic and Geometry, Vol. II , Progr. Math. 36 , Birkhäuser, Basel, 1983, 167-173. Special surfaces, Group actions on varieties or schemes (quotients) Examples of surfaces of general type with vector fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces not numerically effective canonical bundles; deformation; numerical effectiveness; minimal model; ruled surfaces; classification of algebraic threefolds; canonical divisors; extremal rays; equivalence classes of 1- cycles; cone theorem; extremal rational curves on surfaces S. Mori, ''Threefolds whose canonical bundles are not numerically effective,'' Ann. Of Math. (2) 116(1), 133--176 (1982). \(3\)-folds, Divisors, linear systems, invertible sheaves, Minimal model program (Mori theory, extremal rays) Threefolds whose canonical bundles are not numerically effective | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces projective plane; noncommutative graded algebras; regular Koszul algebras of dimension 3 Michael Artin, Geometry of quantum planes, Azumaya algebras, actions, and modules (Bloomington, IN, 1990) Contemp. Math., vol. 124, Amer. Math. Soc., Providence, RI, 1992, pp. 1 -- 15. Noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras), Linear incidence geometry Geometry of quantum planes | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; noncommutative projective line; noncommutative curve; two-sided vector space; noncommutative symmetric algebras; arithmetic noncommutative projective line Nyman, A, The geometry of arithmetic noncommutative projective lines, J. Algebra, 414, 190-240, (2014) Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry The geometry of arithmetic noncommutative projective lines | 1 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cross-correlations of shift register sequences; number of rational places of function fields defined over finite fields; Goppa algebraic-geometric codes; weight distributions; duals of BCH codes G. Garcia, ''Henning Stichtenoth algebraic function fields over finite fields with many rational places, '' IEEE Trans. Info. Theory, IT-41, 1548--1563 (1995). Curves over finite and local fields, Finite ground fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Shift register sequences and sequences over finite alphabets in information and communication theory Algebraic function fields over finite fields with many rational places | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cyclic function fields; \(L\)-functions unctions of functions fields; mean value of \(L\)-functions; zeta functions; function; class number Rosen, M.: Average value of class numbers in cyclic extensions of the rational function field. In: Number Theory. (Halifax, NS, 1994), pp. 307-323, CMS Conference Proceedings, vol. 15. American Mathematical Society, Providence, RI (1995) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Rate of growth of arithmetic functions, Other algebras and orders, and their zeta and \(L\)-functions, Class groups and Picard groups of orders, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Average value of class numbers in cyclic extensions of the rational function field | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(n\)-dimensional crystallographic groups; point groups; lattices; group algebras; rational function fields; birational invariants Farkas, D. R.: Birational invariants of crystals and fields with a finite group of operators. Math. proc. Cambridge philos. Soc. 107, 417-424 (1990) Other geometric groups, including crystallographic groups, Rational and birational maps, Group rings Birational invariants of crystals and fields with a finite group of operators | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces automorphic form; Drinfeld shtuka; Langlands correspondence; moduli stack of shtukas; global Langlands conjecture; function fields Laumon, G.: Chtoucas de Drinfeld et correspondance de Langlands. Gaz. Math. \textbf{88}, 11-33 (2001) Drinfel'd modules; higher-dimensional motives, etc., Langlands-Weil conjectures, nonabelian class field theory, Arithmetic theory of algebraic function fields, Algebraic moduli problems, moduli of vector bundles Drin'feld shtukas and Langlands correspondence (following Laurent Lafforgue) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Arithmetic theory of algebraic functions; Dedekind-Weber theory; algebraic function fields; linear systems; divisors; Abelian differentials Algebraic functions and function fields in algebraic geometry On the theory of algebraic functions of one variable and \textit{Abel}ian integrals | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces division algebras; Brauer groups; rational function fields; ramification maps; central simple algebras A. S. Sivatski, L. H. Rowen and J.-P. Tignol, Division algebras over rational function fields in one variable, in Algebra and Number Theory, Proceedings of the Silver Jubilee Conference 2003, Hindustan Book Agency, New Delhi, 2005, pp. 158--180. Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Division algebras over rational function fields in one variable. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces fields of large transcendence degree; algebraic independence; zero lemmas; zero estimate for group varieties; primary ideal; polynomial rings; algebraic subgroups of products of elliptic curves; effective version of Hilbert's Nullstellensatz; Kolchin theorem; Weierstrass elliptic function Masser, D. W.; Wüstholz, G., Fields of large transcendence degree generated by values of elliptic functions, Invent. Math., 72, 3, 407-464, (1983) Transcendence theory of elliptic and abelian functions, Varieties over global fields, Global ground fields in algebraic geometry Fields of large transcendence degree generated by values of elliptic functions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic geometric codes; geometric Goppa codes; bounds on linear codes; algebraic curves; function fields; tensor rank; multiplication in finite fields; bilinear complexity Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory), Research exposition (monographs, survey articles) pertaining to information and communication theory, Bounds on codes, Computational aspects of algebraic curves, Multilinear algebra, tensor calculus Coding theory and bilinear complexity | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces projective Schur groups; Brauer groups; rational function fields in one variable; cyclic algebras; Kummer extensions; projective Schur algebras; Abelian splitting fields E. Aljadeff and J. Sonn,On the projective Schur group of a field, Journal of Algebra178 (1995), 530--540. Finite-dimensional division rings, Brauer groups of schemes On the projective Schur group of a field | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ruled surfaces; Hilbert schemes of scrolls; moduli; embedded degenerations A. Calabri, C. Ciliberto, F. Flamini, R. Miranda, Non-special scrolls with general moduli. \textit{Rend. Circ. Mat. Palermo} (2) 57 (2008), 1-31. MR2420521 Zbl 1222.14082 Rational and ruled surfaces, Fibrations, degenerations in algebraic geometry, Divisors, linear systems, invertible sheaves, Vector bundles on curves and their moduli, Enumerative problems (combinatorial problems) in algebraic geometry Non-special scrolls with general moduli | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Frobenius manifolds; Hurwitz spaces of moduli of meromorphic functions on Riemann surfaces; isomonodromic tau-function; quadratic Hamiltonian; Gromov-Witten invariants; Bergmann projective connection A. Kokotov and D. Korotkin, On \(G\)-function of Frobenius manifolds related to Hurwitz spaces , Int. Math. Res. Not. 2004 , no. 7, 343--360. Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Compact Riemann surfaces and uniformization, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) On \(G\)-function of Frobenius manifolds related to Hurwitz spaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces automorphism groups of algebraic function fields; realization of group as Galois group; Galois theory Henning Stichtenoth, Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper, Math. Z. 187 (1984), no. 2, 221 -- 225 (German). Separable extensions, Galois theory, Inverse Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces inverse Galois theory; algebraic fundamental group; plane curves; factorization of polynomials; resolution of plane curve singularities; hyperelliptic function fields; construction of Galois extensions; finite group; Galois group; PSL(2,8); unramified covering; affine line Shreeram S. Abhyankar, Square-root parametrization of plane curves, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 19 -- 84. Inverse Galois theory, Special algebraic curves and curves of low genus, Coverings of curves, fundamental group, Coverings in algebraic geometry Square-root parametrization of plane curves. Appendix by J.-P. Serre | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces varieties of singular matrices; global Milnor fibration; classical symmetric spaces; Cartan model; Cartan conjugacy; pseudo-rotations; ordered symmetric and skew-symmetric factorizations; Schubert decomposition; Schubert cycles; Iwasawa decomposition; characteristic subalgebra Complex surface and hypersurface singularities, Discriminantal varieties and configuration spaces in algebraic topology, Homology and cohomology of homogeneous spaces of Lie groups, Determinantal varieties, Representation theory for linear algebraic groups Schubert decomposition for Milnor fibers of the varieties of singular matrices | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Seiberg-Witten equations; ruled surfaces; Kähler metrics; parabolic bundles; stability of bundles Kähler manifolds, Global differential geometry of Hermitian and Kählerian manifolds, Holomorphic bundles and generalizations, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Kähler surfaces of finite volume and Seiberg-Witten equations. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces theta-function; tau-function; classical limit; form factors of fields; Knizhnik-Zamolodchikov equation; finite-gap integration Smirnov F.A. (1993) Form factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration. Commun. Math. Phys. 155, 459--487 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Theta functions and curves; Schottky problem Form factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces graded rings; Artin-Schelter regular algebras of global dimension three; noncommutative projective geometry; elliptic algebras; point modules; Noetherian domains; Hilbert series; elliptic curves -, Algebras associated to elliptic curves , Trans. Amer. Math. Soc. 349 (1997), 2317--2340. JSTOR: Graded rings and modules (associative rings and algebras), Elliptic curves, Noetherian rings and modules (associative rings and algebras), Homological dimension in associative algebras, Noncommutative algebraic geometry, Ordinary and skew polynomial rings and semigroup rings Algebras associated to elliptic curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Calabi-Yau manifolds; strong fields; Hodge theory; nuclear algebraic surfaces; irreducible representation of SO(10); string theory String and superstring theories in gravitational theory, Calabi-Yau manifolds (algebro-geometric aspects) Nuclear algebraic geometry and \(\text{SO}(10)\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces polynomial functors; rational modules; algebraic groups; categories of functors; exponential functors; cohomology of representations; linear algebraic groups over finite fields; polynomial representations; cohomology rings; divided powers; symmetric powers; Ext groups V Franjou, E M Friedlander, A Scorichenko, A Suslin, General linear and functor cohomology over finite fields, Ann. of Math. \((2)\) 150 (1999) 663 Representation theory for linear algebraic groups, Cohomology theory for linear algebraic groups, Projectives and injectives (category-theoretic aspects), Special properties of functors (faithful, full, etc.), Homological methods in group theory, Linear algebraic groups over finite fields, Group schemes, Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) General linear and functor cohomology over finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic function fields; Klein surfaces; formally real fields Gamboa, JM, Compact Klein surfaces with boundary viewed as real compact smooth algebraic curves, Mem. Real Acad. Cienc. Exact. Fís. Nat. Madr., 27, iv+96, (1991) Arithmetic ground fields for curves, Klein surfaces, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Arithmetic theory of algebraic function fields Compact Klein surfaces with boundary viewed as real compact smooth algebraic curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Mordell's conjecture over function fields; theorem of the kernel . Coleman, R.F. , '' Manin's proof of the Mordell conjecture over function fields '', preprint. Rational points, Families, moduli of curves (algebraic), Algebraic functions and function fields in algebraic geometry Manin's proof of the Mordell conjecture over function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic curves over finite fields; discrete elliptic logarithm function; public key cryptosystems; twisted pair of curves Cryptography, Elliptic curves, Arithmetic ground fields for curves On implementing elliptic curve cryptosystems | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Castelnuovo-Mumford regularity; rational points in projective spaces over finite fields; Hilbert function; index of stability E. Kunz and R. Waldi, On the regularity of configurations of \(\mathbb{F}_q\)-rational points in projective space , J. Comm. Alg. 5 (2013), 269-280. Finite ground fields in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Rational points, Finite fields and commutative rings (number-theoretic aspects) On the regularity of configurations of \(\mathbb F_q\)-rational points in projective space | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Humbert surfaces; transcendence properties; automorphic functions; elliptic modular function; families of abelian varieties; complex multiplication points; PEL families Paula Beazley Cohen, Humbert surfaces and transcendence properties of automorphic functions, Rocky Mountain J. Math. 26 (1996), no. 3, 987-1001. Symposium on Diophantine Problems (Boulder, CO, 1994). Transcendence theory of other special functions, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties Humbert surfaces and transcendence properties of automorphic functions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces variations of hodge structures; Toda fields; Liouville gravity; uniformization of Riemann surfaces; vector bundles Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Applications of holomorphic fiber spaces to the sciences, Transcendental methods of algebraic geometry (complex-analytic aspects), Vector bundles on curves and their moduli, Algebraic moduli problems, moduli of vector bundles Toda field theory as a clue to the geometry of \(W_n\)-gravity | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces automorphism groups of function fields; function fields over finite fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Automorphisms of curves, Applications to coding theory and cryptography of arithmetic geometry The asymptotic behavior of automorphism groups of function fields over finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic fibrations; elliptic \(K3\) surfaces; rational elliptic surfaces; fields of definitions of elliptic fibrations Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(K3\) surfaces and Enriques surfaces Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces framed vector bundles; ruled surfaces; instantons; moduli of vector bundles Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Rational and ruled surfaces, Families, moduli, classification: algebraic theory On the structure of moduli spaces of framed vector bundles on rational and ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Weierstraß \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237. Elliptic curves, Rational points, Elliptic curves over local fields, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Elliptic curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces extension of ground fields; elliptic fibration; elliptic surface; function field; conjectures of Birch and Swinnerton-Dyer G. R. Grant and E. Manduchi, Root numbers and algebraic points on elliptic surfaces with base \(\mathbbP^1\) , Duke Math. J. 89 (1997), no. 3, 413-422. Rational points, Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Root numbers and algebraic points on elliptic surfaces with base \(\mathbb{P}^1\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces complex conjugation; number of connected components; symmetric surfaces; real plane curves; genus; separating number Topology of real algebraic varieties, Plane and space curves Topology of real algebraic curves: A Felix Klein question | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces sum of divisors function; symmetric group; permutation John R. Britnell, A formal identity involving commuting triples of permutations, J. Combin. Theory Ser. A 120 (2013), no. 4, 941 -- 943. Arithmetic functions; related numbers; inversion formulas, Permutations, words, matrices, Special sequences and polynomials, Coverings of curves, fundamental group A formal identity involving commuting triples of permutations | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces deformation of complete intersection; Hilbert function; Artin algebras; peelable algebras Iarrobino, A.: Deforming complete intersection Artin algebras, appendix: Hilbert function of C[x,y]/I. Proc. sympos. Pure math. 40 (1983) Deformations and infinitesimal methods in commutative ring theory, Complete intersections, Commutative Artinian rings and modules, finite-dimensional algebras, Formal methods and deformations in algebraic geometry, Polynomial rings and ideals; rings of integer-valued polynomials, Formal power series rings Deforming complete intersection Artin algebras. Appendix: Hilbert function of \({\mathbb{C}}[x,y]/I\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces diophantine equations; equations over finite fields; arithmetic theory of algebraic curves; nonstandard arithmetic; zeta function; integral points on curves S. A. Stepanov, \textit{Arithmetic of Algebraic Curves} (Nauka, Moscow, 1991) [in Russian]. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Curves over finite and local fields, Arithmetic ground fields for curves, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Rational points Arithmetic of algebraic curves. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic number theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. Research exposition (monographs, survey articles) pertaining to number theory, Class field theory, Class field theory; \(p\)-adic formal groups, Ramification and extension theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Collected or selected works; reprintings or translations of classics Algebraic numbers and algebraic functions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Dirichlet \(L\)-functions; moments of \(L\)-functions; function fields; finite fields; random matrix theory Zeta and \(L\)-functions in characteristic \(p\), Polynomials over finite fields, Relations with random matrices, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of polynomial rings over finite fields The integrated fourth moment of Dirichlet \(L\)-functions over rational function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces combinatorial Hopf algebras; noncommutative symmetric functions; quasisymmetric functions; Malvenuto-Reutenauer Hopf algebras; dualities; coproducts; Grothendieck polynomials; K-theory; Schubert varieties; generating series; set-valued tableaux; Schur functions; bialgebras Lam, Thomas; Pylyavskyy, Pavlo, Combinatorial Hopf algebras and \(K\)-homology of grassmanians, Int. Math. Res. Not., 2007, 24, (2007) Hopf algebras and their applications, Connections of Hopf algebras with combinatorics, Symmetric functions and generalizations, Grassmannians, Schubert varieties, flag manifolds Combinatorial Hopf algebras and \(K\)-homology of Grassmanians. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic-geometry codes; towers of function fields; \(Q\)th-power map Leonard, D. A.: Finding the missing functions for one-point AG codes. IEEE trans. Inform. theory 47, No. 6, 2566-2573 (2001) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic theory of algebraic function fields Finding the defining functions for one-point algebraic-geometry codes | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces reconstruction theorem; abelian category; noncommutative algebraic geometry; quasi-coherent sheaves; automorphism class group; quasi-separated scheme; the spectrum of $\mathcal A$; equivalence of groupoids; automorphism class group; derived category of coherent sheaves; tensor triangulated category of perfect complexes; Tannaka duality Rosenberg's reconstruction theorem | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cartography; plane trees; Belyi functions; unicellular dessin; function fields of algebraic curves N. Adrianov and G. Shabat, ''Unicellular cartography and Galois orbits of plane trees,'' in: \textit{Geometric Galois Actions}, 2, (1997), pp. 13-24. Enumerative problems (combinatorial problems) in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Group actions on varieties or schemes (quotients) Unicellular cartography and Galois orbits of plane trees | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces towers of algebraic function fields; genus; number of places Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Finite ground fields in algebraic geometry On a tower of Garcia and Stichtenoth | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces valued function fields; good reduction; regular functions; reciprocity lemma; unit; local symbols; local-global principle; solvability of diophantine equations P. Roquette, \textsl Reciprocity in valued function fields, Journal für die reine und angewandte Mathematik 375/376 (1987), 238--258. Arithmetic theory of algebraic function fields, Valued fields, Algebraic functions and function fields in algebraic geometry, Diophantine equations Reciprocity in valued function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces quiver varieties; Kac-Moody algebras; moduli space of sheaves on surfaces Schiffmann, O., Variétés carquois de Nakajima (d'après Nakajima, Lusztig, varagnolo, vasserot, crawley-boevey, et al.), Astérisque, 311, 295-344, (2008), Séminaire Bourbaki, vol. 2006/2007, Exp. No. 976 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Representations of quivers and partially ordered sets Nakajima's quiver varieties (after Nakajima, Lusztig, Varagnolo, Vasserot, Crawley-Boevey, et al.) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetry of cubic surfaces in Euclidean space; skew symmetry Euclidean geometries (general) and generalizations, Special surfaces Some cubic surfaces with an infinite set of planes of skew-symmetry | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces coherent rings; graded algebras; noncommutative schemes; Gorenstein algebras; categories of coherent modules; coherent sheaves D. Piontkovski, Coherent algebras and noncommutative projective lines. J. Algebra 319 (2008), 3280-3290. Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras), Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) Coherent algebras and noncommutative projective lines. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces differential operators; commutative affine \({\mathbb{C}}\)-algebra; coordinate ring; nonsingular affine variety; simple noetherian domain; Gelfand- Kirillov dimension; ring of invariants; group of automorphisms; simple noetherian ring; variety of symmetric n\(\times n\) matrices; simple factor ring; enveloping algebras; semisimple Lie algebras Levasseur, T.; Stafford, J. T., Rings of differential operators on classical rings of invariants, Mem. Amer. Math. Soc., 412, pp., (1989) Noetherian rings and modules (associative rings and algebras), Group actions on varieties or schemes (quotients), Universal enveloping (super)algebras, Infinite-dimensional simple rings (except as in 16Kxx), Determinantal varieties, Automorphisms and endomorphisms, Valuations, completions, formal power series and related constructions (associative rings and algebras), Simple, semisimple, reductive (super)algebras, Modules of differentials, Geometric invariant theory, Sheaves of differential operators and their modules, \(D\)-modules Rings of differential operators on classical rings of invariants | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces complex algebraic semisimple adjoint groups; smooth complete symmetric varieties; intersection cohomology complexes; extension algebras; derived categories; dg-algebras; categories of sheaves Guillermou, S.: Equivariant derived category of a complete symmetric variety. Represent. Theory 9, 526--577 (2005) Differential graded algebras and applications (associative algebraic aspects), Equivariant homology and cohomology in algebraic topology, Derived categories and associative algebras, Group actions on varieties or schemes (quotients), Cohomology theory for linear algebraic groups Equivariant derived category of a complete symmetric variety. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces arithmetic theory of algebraic function fields; towers of function fields; Zink's bound; Hasse-Witt invariant; \(p\)-rank [2]A. Bassa and P. Beelen, The Hasse--Witt invariant in some towers of function fields over finite fields, Bull. Brazil. Math. Soc. 41 (2010), 567--582. Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry The Hasse-Witt invariant in some towers of function fields over finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite-dimensional central division algebras; rational function fields; relative Brauer groups; Picard groups DOI: 10.1016/j.jpaa.2010.06.030 Brauer groups (algebraic aspects), Brauer groups of schemes, Finite-dimensional division rings, Picard groups The relative Brauer group of a cyclic cover of affine space. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces isotropy; local-global principle; real field; sums of squares; \(u\)-invariant; pythagoras number; valuation; algebraic function fields Becher, Karim; Grimm, David; Van Geel, Jan: Sums of squares in algebraic function fields over a complete discretely valued field, Pacific J. Math. 267, No. 2, 257-276 (2014) Quadratic forms over general fields, Forms over real fields, Sums of squares and representations by other particular quadratic forms, Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Transcendental field extensions, Algebraic functions and function fields in algebraic geometry Sums of squares in algebraic function fields over a complete discretely valued field | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Young diagram; standard bases; symmetric tensor; skew symmetric tensor; invariant theory Rota, G.-C. \& Stein, J. A., Symbolic method in invariant theory, Proc. Natl. Acad. Sci. USA, 83 (1986), 844-847. Vector and tensor algebra, theory of invariants, Geometric invariant theory, Enumerative combinatorics Symbolic method in invariant theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces function field of elliptic curve; Witt ring; elliptic curve; generators; relations; symmetric bilinear spaces; cohomological invariants; Grothendieck ring; étale cohomology groups Arason, J. K.; Elman, R.; Jacob, B.: On the Witt ring of elliptic curves, Proc. symp. Pure math. 58, No. Part II, 1-25 (1995) Algebraic theory of quadratic forms; Witt groups and rings, Elliptic curves, Étale and other Grothendieck topologies and (co)homologies, Other nonalgebraically closed ground fields in algebraic geometry, Vector bundles on curves and their moduli On the Witt ring of elliptic curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic function; maximal-commutative algebras in the ring of differential operators; finite-gap solution Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to ordinary differential equations, Research exposition (monographs, survey articles) pertaining to partial differential equations, Relationships between algebraic curves and integrable systems, Commutative rings of differential operators and their modules, Lamé, Mathieu, and spheroidal wave functions, Entire and meromorphic solutions to ordinary differential equations in the complex domain Commuting differential operators with elliptic coefficients | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tower of function fields; genus; rational places; curves with many points A. Garcia, H. Stichtenoth, On the Galois closure of towers, preprint, 2005 Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Asymptotics for the genus and the number of rational places in towers of function fields over a finite field | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Galois groups of function fields; unramified cohomology; universal spaces; anabelian geometry Galois cohomology, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Cohomology of groups Universal spaces for unramified Galois cohomology | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces super Riemann surfaces; dressed moduli spaces; Picard group; Picard functor; Picard variety; abelian conformal field theory; vertex operator algebra; Heisenberg algebra; conformal blocks; theta functions of higher level; infinite-dimensional Lie algebras; supercurves; Beilinson-Bernstein localization; Fock representation Virasoro and related algebras, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Riemann surfaces, Algebraic functions and function fields in algebraic geometry, Theta functions and abelian varieties, Families, moduli of curves (algebraic) Abelian conformal field theory and \(N=2\) supercurves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces complex multiplication; \(K3\) surfaces; fields of definition; class field theory \(K3\) surfaces and Enriques surfaces, Complex multiplication and moduli of abelian varieties, Brauer groups of schemes, Special surfaces, Automorphisms of surfaces and higher-dimensional varieties Fields of definition of \(K3\) surfaces with complex multiplication | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces unramified cohomology; Brauer groups; central division algebras; exponents; indices; smooth projective varieties; biquaternion algebras; function fields Colliot-Thélène, J.-L., Exposant et indice d'algèbres simples centrales non ramifiées, Enseign. Math. (2), 48, 1-2, 127-146, (2002) Finite-dimensional division rings, Brauer groups of schemes, Skew fields, division rings Exponent and index of nonramified central simple algebras (with an appendix by Ofer Gabber). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Galois closure; ring extensions; algebras of finite rank; finite étale algebra; symmetric Galois group Galois theory and commutative ring extensions, Projective and free modules and ideals in commutative rings, Local structure of morphisms in algebraic geometry: étale, flat, etc. The Galois closure for rings and some related constructions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces scrolls; multiple coverings of ruled rational complex surfaces Coverings in algebraic geometry, Rational and unirational varieties Multiple coverings of rational ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces projective complex varieties; cohomology groups; Brauer groups; function fields; quaternion algebras; biquaternion division algebras; Azumaya algebras; equivariant cohomology Andrew Kresch, Hodge-theoretic obstruction to the existence of quaternion algebras, Bull. London Math. Soc. 35 (2003), no. 1, 109 -- 116. Brauer groups (algebraic aspects), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Brauer groups of schemes Hodge-theoretic obstruction to the existence of quaternion algebras | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces polynomial automorphisms; tame automorphisms; affine spaces over finite fields; automorphism group; bijections; set of zeros; primitive subgroup of the symmetric group S. Maubach, Polynomial automorphisms over finite fields, Serdica Math. J. 27 (2001), no. 4, 343--350. Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Polynomials over finite fields, Polynomials in number theory, Primitive groups, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Infinite automorphism groups, Jacobian problem Polynomial automorphisms over finite fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces towers of algebraic function fields; genus; number of places Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Quadratic recursive towers of function fields over \(\mathbb{F}_2\) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces stability; vector bundle; symmetric power; ruled surface; cone of curves Vector bundles on curves and their moduli, Rational and ruled surfaces Stability of symmetric powers of vector bundles of rank two with even degree on a curve | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces covering of stable genus three curves; fibre of Prym map; abelian surface; symmetric theta divisor; Satake compactification of the moduli space of principally polarized abelian surfaces Verra, A.: The fiber of the Prym map in genus 3. Math. Ann. 276, 433--448 (1987) Algebraic moduli of abelian varieties, classification, Families, moduli of curves (algebraic), Theta functions and abelian varieties The fibre of the Prym map in genus three | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces curve over a global field; \(K_1\); local class field theory of curves; Galois cohomology; surfaces over finite fields Wayne Raskind, On \?\(_{1}\) of curves over global fields, Math. Ann. 288 (1990), no. 2, 179 -- 193. Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic ground fields for curves, Global ground fields in algebraic geometry, \(K\)-theory in geometry On \(K_1\) of curves over global fields. Appendix by C. Weibel | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ruled degenerations of minimal ruled surfaces; conic bundles Rational and ruled surfaces, Formal methods and deformations in algebraic geometry, Families, moduli, classification: algebraic theory Degenerations of minimal ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces division algebras; reduced norms; function field of \(p\)-adic curves; Galois cohomology Galois cohomology of linear algebraic groups, Curves over finite and local fields, Galois cohomology, Algebraic functions and function fields in algebraic geometry, Finite-dimensional division rings Local-global principle for reduced norms over function fields of \(p\)-adic curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces first order theory of function fields in the language of fields; curves; undecidability Jean-Louis Duret, Sur la théorie élémentaire des corps de fonctions, J. Symbolic Logic 51 (1986), no. 4, 948 -- 956. Model-theoretic algebra, Model theory of fields, Decidability and field theory, Curves in algebraic geometry Sur la théorie élémentaire des corps de fonctions. (On the elementary theory of function fields) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic geometric codes; towers of function fields Geometric methods (including applications of algebraic geometry) applied to coding theory, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Applications to coding theory and cryptography of arithmetic geometry Integral bases in a tower of function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces deformation theory; graph complexes; deformation complexes; Grothendieck-Teichmüller; Lie algebra; Operad; tensor algebras; fedosov resolution; polyvector fields; Maurer-Cartan equation; Grothendieck-Teichmüller group; twisting operads Dolgushev, V., Rogers, C.L., Willwacher, T.: Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields (2012). arxiv:1211.4230 Group actions on varieties or schemes (quotients), Structure theory for Lie algebras and superalgebras, Universal enveloping (super)algebras, Homological methods in Lie (super)algebras Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric product; resolution of singularities; generating function Borisov L and Libgober A 2003 Elliptic genera of singular varieties \textit{Duke Math. J.} 116 319--51 Calabi-Yau manifolds (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties, Modifications; resolution of singularities (complex-analytic aspects), Elliptic cohomology, Relations with algebraic geometry and topology Elliptic genera of singular varieties. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative generalizations of polynomial algebras; coordinate algebras; noncommutative differential geometry; noncommutative algebraic geometry Dubois-Violette, M.: Noncommutative coordinate algebras. In: Blanchard, E. (ed.) Quanta of Maths, dédié à à A. Connes. In: Clay Mathematics Proceedings, pp. 171--199. Clay Mathematics Institute (2010) Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Quadratic and Koszul algebras, Ordinary and skew polynomial rings and semigroup rings, Graded rings and modules (associative rings and algebras) Noncommutative coordinate algebras. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces compactification of projective 3-space; singular K-3 surfaces; hypersurface isolated singularity; ruled surface; exceptional curves; Fano 3-fold . M. Furushima , Singular K3 surfaces with hypersurface singularities , Pacific J. Math. 125 (1986) 67-77. Singularities of surfaces or higher-dimensional varieties, Compact complex surfaces, Moduli, classification: analytic theory; relations with modular forms, Singularities in algebraic geometry, Families, moduli, classification: algebraic theory, Automorphisms of surfaces and higher-dimensional varieties, \(3\)-folds On the singular K-3 surfaces with hypersurface singularities | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces recursively axiomatized class; pseudo real closed fields; strongly pseudo real closed; totally transcendental; totally real; Hilbertian fields; Hilbert's irreducibility theorem; model complete; model companionable; elimination of quantifiers; decidable; orderings; Nullstellensätze; function field; holomorphy ring; Prüfer ring; generalized Jacobson ring; p-adically closed fields DOI: 10.1007/BF03322485 Field extensions, Model theory of fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Decidability of theories and sets of sentences, Model-theoretic algebra, Ordered fields, Quantifier elimination, model completeness, and related topics, Algebraic number theory: local fields, Dedekind, Prüfer, Krull and Mori rings and their generalizations On some classes of Hilbertian fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces meromorphic functions; number field analogue of Nevanlinna's five-valued theorem counting multiplicities; uniqueness polynomials for complex meromorphic functions; non-Archimedean meromorphic functions; algebraic function fields Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Algebraic functions and function fields in algebraic geometry, Non-Archimedean function theory Uniqueness polynomials, unique range sets and other uniqueness theorems | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces semiprime graded algebras; Noetherian rings; Gelfand-Kirillov dimension; twisted homogeneous coordinate rings; Veronese rings; noncommutative projective geometry; noncommutative projective curves; algebras of quadratic growth Artin, M.; Stafford, J. T., Semiprime graded algebras of dimension two, J. Algebra, 227, 1, 68-123, (2000) Graded rings and modules (associative rings and algebras), Noetherian rings and modules (associative rings and algebras), Growth rate, Gelfand-Kirillov dimension, Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Finite rings and finite-dimensional associative algebras Semiprime graded algebras of dimension two | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(K3\) surfaces; modular invariance of complex manifolds; vanishing first Chern class; Neveu-Schwarz superalgebra; 3-folds; Calabi-Yau spaces; Jacobi function; Fermat type hypersurface; Witten's index; elliptic genus DOI: 10.1142/S0129167X92000151 Algebraic topology on manifolds and differential topology, Compact complex \(3\)-folds, Algebraic moduli problems, moduli of vector bundles, Other homology theories in algebraic topology Modular invariance of manifolds with \(SU(n)\) holonomy | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Witt rings of function fields; real analytic manifold; second residue class homomorphism; Artin-Lang property; Witt group of the ring of real analytic functions Algebraic theory of quadratic forms; Witt groups and rings, Real-analytic and semi-analytic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) On Witt rings of function fields of real analytic surfaces and curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tame algebras; symmetric special biserial algebras; gentle algebras; trivial extensions; Brauer graph algebras; admissible cuts; marked Riemann surfaces; triangulations Schroll, S., Trivial extensions of gentle algebras and Brauer graph algebras, J. Algebra, 444, 183-200, (2015) Representations of quivers and partially ordered sets, Representation type (finite, tame, wild, etc.) of associative algebras, Cluster algebras, Riemann surfaces; Weierstrass points; gap sequences, Representations of associative Artinian rings Trivial extensions of gentle algebras and Brauer graph algebras. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 1996. Rational points, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Elliptic curves Mordell-Weil groups in procyclic extensions of a function field | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces automorphism groups of affine varieties; ind-groups; Lie algebras of ind-groups; vector fields; affine \(n\)-spaces Group actions on varieties or schemes (quotients), Geometric invariant theory, Other algebraic groups (geometric aspects), Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Group actions on affine varieties, Automorphisms, derivations, other operators for Lie algebras and super algebras, Infinite-dimensional Lie (super)algebras, Lie algebras of vector fields and related (super) algebras, Representation theory for linear algebraic groups Automorphism groups of affine varieties and a characterization of affine \(n\)-space | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(\mu\)-stable; Grothendieck-Riemann-Roch; Donaldson polynomials; moduli space of rank two bundles on ruled surfaces Algebraic moduli problems, moduli of vector bundles, Characteristic classes and numbers in differential topology, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Fine and coarse moduli spaces Symmetric polynomials constructed from moduli of stable sheaves with odd \(c_ 1\) on ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Semi-stable and stable vector bundles on regular projective curves; moduli space of stable bundles; local non-abelian zeta functions for curves defined over finite fields (rationality and functional equations); global non-abelian zeta functions for curves defined over number fields; non-abelian L--functions for function fields (rationality and functional equations) Weng, L.: Non-abelian L function for number fields Zeta and \(L\)-functions in characteristic \(p\), Other Dirichlet series and zeta functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Vector bundles on curves and their moduli Non-abelian zeta functions for function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces transcendence of zeta values; function fields Transcendence (general theory), Zeta functions and \(L\)-functions of number fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Report on transcendency in the theory of function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912). Abstract differential equations, Birational automorphisms, Cremona group and generalizations, History of field theory, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies Birational automorphism groups and differential equations | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Weierstrass function; lattices; cubic polynomials; geometric realization of hyperelliptic curves; symmetric \(4p\)-gons; polynomials with nonzero discriminant; biholomorphism; Picard-Fuchs equation; hyperelliptic Riemann surface Compact Riemann surfaces and uniformization, Elliptic curves, Families, moduli of curves (analytic) Geometric realizations of hyperelliptic curves. II | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces graded algebras; global dimension; projective surfaces; noncommutative surfaces; AS-Gorenstein algebras D. Rogalski and S.J. Sierra, Some noncommutative projective surfaces of GK-dimension 4, Compos. Math. \textbf{148} (2012), 1195-1237. Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras), Growth rate, Gelfand-Kirillov dimension, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) Some projective surfaces of GK-dimension 4 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces counting function; bounded height; upper bound; algebraic surface; number of rational points; nonsingular cubic surfaces; nonsingular quartic surfaces Varieties over global fields, Rational points, Counting solutions of Diophantine equations Counting rational points on cubic and quartic surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces formal groups; quantum groups; categories of noncommutative formal power series algebras; cogroup objects; topological Hopf algebras; quantum group law chunks Holtkamp, R.: On formal quantum group laws. Arch. math. 73, 90-103 (1999) Formal groups, \(p\)-divisible groups, Valuations, completions, formal power series and related constructions (associative rings and algebras), Quantum groups (quantized enveloping algebras) and related deformations, Bordism and cobordism theories and formal group laws in algebraic topology On formal quantum group laws | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces efficiency of function field sieve; discrete logarithms in finite fields; supersingular elliptic curves Granger, R., Holt, A., Page, D., Smart, N.P., Vercauteren, F.: Function field sieve in Characteristic three.In: Algorithmic Number Theory Symposium - ANTS VI, pp. 223--234. Springer LNCS 3076 (2004) Algebraic coding theory; cryptography (number-theoretic aspects), Number-theoretic algorithms; complexity, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Function field sieve in characteristic three | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic surfaces; intersection theory; singularities; ruled surfaces; quasielliptic fibrations; minimal model theory; canonical dimension; Enriques-Kodaira classification of algebraic surfaces; characteristic \(p\); elliptic fibrations; rational surfaces Bădescu, L., Algebraic surfaces, Universitext, (2001), Springer-Verlag New York, Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author. MR 1805816 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Surfaces and higher-dimensional varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Fibrations, degenerations in algebraic geometry, Families, moduli, classification: algebraic theory Algebraic surfaces. Transl. from the Romanian by V. Maşek | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tensor powers of the Carlitz module; zeta values; motive; Tannakian category; conjectures of D. Zagier; multilogs; \(\zeta\)-functions of number fields Anderson, G.; Thakur, D., \textit{tensor powers of the Carlitz module and zeta values}, Ann. of Math. (2), 132, 159-191, (1990) Arithmetic theory of algebraic function fields, Drinfel'd modules; higher-dimensional motives, etc., Generalizations (algebraic spaces, stacks), Global ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Applications of methods of algebraic \(K\)-theory in algebraic geometry Tensor powers of the Carlitz module and zeta values | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative deformation theory; time-space; dirac derivation; phase space; non-commutative scheme; representations of associative algebras; dynamical structure; interaction; algebraic quantum fields; connections Research exposition (monographs, survey articles) pertaining to algebraic geometry, Noncommutative algebraic geometry, Noncommutative geometry in quantum theory, Representation theory of associative rings and algebras Geometry of time-spaces. Non-commutative algebraic geometry, applied to quantum theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces constructibility of the helices of period four; ruled rational surfaces; Markov type diophantine equations; exceptional sheaves Д. Ю. Ногин, ``Спирали периода четыре и уравнения типа Маркова'', Изв. АН СССР. Сер. матем., 54:4 (1990), 862 -- 878 Rational and ruled surfaces, Quadratic and bilinear Diophantine equations, Efficient generation of modules, Rational points, Vector bundles on surfaces and higher-dimensional varieties, and their moduli Helices of period four and an equation of Markov type | 0 |