Datasets:

AnkitSatpute

/

zbMath_kwrdref

like 0

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Galois action; Mordell-Weil group doi:10.4064/aa108-1-3

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(p\)-adic deformations; cusp forms; functional equation of \(L\)-series; order of vanishing of the \(L\)-function; elliptic curve; Mordell-Weil group; Selmer group; Birch and Swinnerton-Dyer conjecture Greenberg, R.: Elliptic curves and p-adic deformations. In: Kisilevsky, H., Ram Murty, M. (eds.) Elliptic Curves and Related Topics. CRM Proceedings and Lecture Notes, vol. 4, pp. 101--110. American Mathematical Society, Providence, RI (1994)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational points of affine variety; Hasse principle; ring of all algebraic integers; capacity theory on algebraic curves; completely valued algebraically closed fields; Hilbert's tenth problem; decision procedure for diophantine equations Rumelv, R. S., Arithmetic over the ring of all algebraic integers, Journal für die Reine und Angewandte Mathematik, 368, 127-133, (1986)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mots; words; trees; permutations; toric variety; Weyl chambers; semigroups; Lie algebra; Burnside problem for semigroups; symmetric group; skew tableaux; hypermaps; combinatorial theory; representations; continued fractions; differential algebra; probability measures; grammars of zigzags; complexity; finite automaton M. Lothaire , Mots . Hermès Paris 1990 . MR 1252659 | Zbl 0862.05001

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) finite dimensional representation; symmetric algebra; stable isomorphism; invariant fields; reductive linear groups; division algebras; function field; Brauer-Severi variety David J. Saltman, Invariant fields of linear groups and division algebras, Perspectives in ring theory (Antwerp, 1987) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 233, Kluwer Acad. Publ., Dordrecht, 1988, pp. 279 -- 297.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; group scheme; finite field; arithmetic statistics

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hurwitz curve; automorphism group; Jacobian; point counting

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) free group; conjugacy class; character variety; finite field; \(E\)-polynomial 3. S. Cavazos and S. Lawton, E-polynomial of SL2(\mathbb{C})-character varieties of free groups, Internat. J. Math.25(6) (2014), Article ID:1450058, 27pp, arXiv:1401.0228 [arXiv] . [Abstract] genRefLink(128, 'S0129167X15501001BIB3', '000343050000007');

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) volume density property; vector field; linear algebraic group; affine variety Shulim Kaliman, Frank Kutzschebauch & Matthias Leuenberger, ''Complete algebraic vector fields on affine surfaces'', , 2014

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) function field; Hurwitz genus formula; nilpotent group; positive characteristic

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; finite field; endomorphism ring; rational points

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) quadric; intersection of quadrics; derived category; semiorthogonal decomposition; Clifford algebra; Morita theory; Brauer group; rationality; del Pezzo surface; Fano threefold A. Auel, M. Bernardara and M. Bolognesi, Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems, J. Math. Pures Appl. (9) 102 (2014), 249-291.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Jacobian; Weil polynomial; isogeny class; finite field; abelian surfaces M. E. Zieve and P. Müller, On Ritt's polynomial decomposition theorems , preprint, [math.AG] 0807.3578v1

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil group of elliptic curve

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Calabi-Yau spaces; monodromy; fundamental group; quintic threefolds; braid group; Gauß-Manin connection; supersymmetric conformal field theory

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) reductive group on affine space; variety diffeomorphic to affine space; fixed point; groups which act smoothly on homotopy spheres with exactly one fixed point; icosahedral group; real algebraic action; G-cobordant to a real algebraic G-variety; G-diffeomorphic to a real algebraic G- variety; Poincaré homology sphere; equivariant surgery Dovermann, K. H.; Masuda, M.; Petrie, T.: Fixed point free algebraic actions on varieties diffeomorphic to rn. Topological methods in algebraic transformation groups 80, 49-80 (1989)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) two dimensional global fields; algebraic function field in one; variable over algebraic number field; Galois cohomology group; \(H^ 3\); Hasse principles; local-global principles; reduced norms; division algebras; quadratic forms; sum of squares K.~Kato, {A {H}asse principle for two dimensional global fields. With an appendix by {J}.-{L} {C}olliot-{T}hélène.}, J. Reine Angew. Math. {366} (1986), 142--180. DOI 10.1515/crll.1986.366.142; zbl 0576.12012; MR0833016

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) annihilator; anticyclotomic \(\mathbb{Z}_ p\)-extension of an imaginary quadratic field; modular elliptic curve; Heegner points; Selmer group; Iwasawa theory M. Bertolini , An annihilator for the p-Selmer group by means of Heegner points . Atti Acc. Naz. Lincei, Classe di Sc. Fis., Mat. e Nat., Rendiconti Lincei, Mat. e Appl. , Serie 9 , Vol. 5 , Fasc. 2 ( 1994 ), 129 - 140 . MR 1292568 | Zbl 0853.11049

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) finite field; Jacobian; algebraic function field; class number; tower

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Kleinian group; Jacobian; automorphism; abelian variety

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(p\)-adic heights; abelian variety; adjoint module; \(p\)-adic \(L\)-function; Tate-Shafarevich group; Artin-Mazur duality theory; descent; supersingular reduction -, Duality theorems for abelian varieties over \(\operatorname{\mathbb{Z} }_p\)-extensions, Advanced Studies in Pure Mathematics 17, Algebraic Number Theory-in honour of K. Iwasawa pp. 471-492, 1989.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) ordinary K 3 surface over a finite field; Tate conjecture on algebraic cycles; canonical lifting; abelian variety; Galois representation; rational Hodge structure; Hodge structures Borel, A., Tits, J.: Groupes Réductifs. Inst. Hautes Étud. Sci. Publ. Math. \textbf{27}(1), 55-150 (1965)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) finite field; finite group of automorphisms; Artin L-function; total degree

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Griffiths ring; Jacobian ideal; complete intersection in Grassmann; Hodge group; Cayley trick

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) subschemes; limit of join variety; normal cone; intersection theory; complete intersection; linkage; singularities Flenner, H.; Ulrich, B.; Vogel, W., On limits of joins of maximal dimension, Math. Ann., 308, 2, 291-318, (1997)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) affine algebraic varieties; projective varieties; algebraic schemes; rational algebraic functions; singularities; intersection theory; complete intersections; Gorenstein varieties Kunz, E., Einführung in die algebraische geometrie, (1997), Vieweg Braunschweig/Wiesbaden

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) hyperplane section of curve; curves on hyperplanes; Galois group of function field; incidence; trisecant lemma E. Ballico, On the general hyperplane section of a curve in char. p, Rendiconti Istit. Mat. Univ. Trieste 22 (1990), 117--125.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) reciprocity; duality; motivic cohomology group; higher dimensional class field theory; Hasse principle; Brauer-Grothendieck group S. Saito, ''Some observations on motivic cohomology of arithmetic schemes,'' Invent. math., vol. 98, iss. 2, pp. 371-404, 1989.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) modular Jacobian variety \(J_1(N)\); \(\mu\)-type subgroup; cyclotomic field

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Igusa compactification; Siegel modular variety; moduli space of genus 2 curves; Weierstrass points; zeta function; characteristic p; Weil conjectures Ronnie Lee and Steven H. Weintraub, Cohomology of a Siegel modular variety of degree 2, Group actions on manifolds (Boulder, Colo., 1983) Contemp. Math., vol. 36, Amer. Math. Soc., Providence, RI, 1985, pp. 433 -- 488.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Lang conjecture; rational point; Mordell conjecture; arithmetic abelian varieties; subvarieties; translates of abelian subvarieties Faltings, G.; The general case of S. Lang's conjecture; Barsotti Symposium in Algebraic Geometry: San Diego, CA, USA 1994; ,175-182.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) real algebraic geometry; Gaussian field; harmonic polynomials; critical point theory; Hilbert's sixteenth problem Fyodorov, Yan V.; Lerario, Antonio; Lundberg, Erik, On the number of connected components of random algebraic hypersurfaces, J. Geom. Phys., 95, 1-20, (2015)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) vector bundles; conformal quantum field theory; Verlinde formula; Hilbert functions of moduli spaces of semi-stable vector bundles; compact Riemann surface; generalized theta bundle; Witten conjecture; intersection theory of moduli spaces of algebraic curves; topological field theories; fusion algebras Szenes, A.: The combinatorics of the Verlinde formulas In: Vector Bundles in Algebraic Geometry, Hitchin, N.J., et al., (eds.), Cambridge University Press, 1995

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) simply connected simple algebraic group; algebraic number field; valuations; completion; group of K-rational points; S-arithmetic topology; S-congruence topology; congruence kernel; congruence conjecture; exceptional groups; anisotropic K-group Rapinchuk A S, On the congruence subgroup problem for algebraic groups,Dokl. Akad. Nauk. SSSR 306 (1989) 1304--1307

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Lubin-Tate group; local analog of Kronecker-Weber theorem; maximal unramified extension; local class field theory; maximal abelian extension Gold ( R. ) .- Local class field theory via Lubin-Tate groups , Indiana Univ. Math. J. 30, p. 795 - 798 ( 1981 ). MR 625603 | Zbl 0596.12014

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Mordell-Weil group Kisilevsky, H., Rank determines semi-stable conductor, J. Number Theory, 104, 2, 279-286, (2004)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) plane quartic curves; function field; Galois group K. Miura - H. Yoshihara, Field theory for function fields of plane quartic curves, J. Algebra, 226 (2000), pp. 283-294. Zbl0983.11067 MR1749889

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) product; composition; fuzzy ideal; fuzzy algebraic variety; fuzzy intersection equations; algorithm; fuzzy graph theory; fuzzy commutative algebra Mordeson, J. N.; Chang-Shyh, P.: Fuzzy intersection equations. Fss 60, 77-81 (1993)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Thom-Porteous formula; coherent sheaves; degeneracy class; Chow group; residual intersection; Deligne-Mumford compactification; Fitting ideals; excess intersection theory Bleier, T.: Excess porteous, coherent porteous, and the hyperelliptic locus in m\bar{}3. Mich. math. J. 61, No. 2, 359-383 (2012)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebra of invariants; reductive group action; complete intersection; spherical variety; deformation Panyushev D.: On deformation method in invariant theory. Ann. Inst. Fourier Grenoble 47(4), 985--1012 (1997)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) representation theory; reductive algebraic groups; simple modules; highest weights; character formulas; Weyl's character formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology rings; rings of regular functions; Schubert schemes; line bundles; Schur algebras; quantum groups; Kazhdan-Lusztig polynomials J. C. Jantzen, \textit{Representations of Algebraic Groups. Second edition}, Amer. Math. Soc., Providence (2003).

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) local points; Mordell-Weil group; modular curve; elliptic curve Douglas L. Ulmer, A construction of local points on elliptic curves over modular curves, Internat. Math. Res. Notices 7 (1995), 349 -- 363.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Schubert variety; variation of Hodge structure; infinitesimal period relation; Griffiths' transversality; Hodge theory; Mumford-Tate group Robles, C., \textit{Schubert varieties as variations of Hodge structure}, Selecta Math. (N.S.), 20, 719-768, (2014)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) superelliptic curve; Jacobian variety; twist theory

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hecke operators on Hilbert varieties; estimates of eigenvalues; Hecke ring; Hilbert modular variety; \(\ell\)-adic cohomology; local zeta function; toroidal compactifications; Weil conjecture K. Hatada: On the local zeta functions of compactified Hilbert modular schemes and action of the Hecke rings. Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci., 18, no. 2, 1-34 (1994).

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; abelian function; soliton; theta type; commutative group varieties; hyperfields I. Barsotti , Le equazioni differenziali delle funzioni theta , Rend. Accad. Naz. XL , 101 , 1983 , p. 227 .

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) fixed point set; flag variety; unipotent element; irreducible components; Young tableaux; Kazhdan-Lusztig polynomials; intersection codimensions; Jordan blocks J.Wolper, Some intersection properties of the fibres of Springer's resolution, Proc. Am. Math. Soc. 91 (1984), 182--188.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) deformation theory of isolated hypersurface singularities; small resolution; generalized Fano variety; threefold with trivial dualizing sheaf; maximum number of nodes; rational curves of low degree on quintic threefolds Losev, A., Nekrasov, N., Shatashvili, S.: \textit{Testing Seiberg-Witten solution}. In: Strings, branes and dualities (Cargèse, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. \textbf{520}. Dordrecht: Kluwer Acad. Publ., 1999, pp. 359-372

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curve; Weil height; canonical height; Mordell-Weil group Silverman, J.H.; The difference between the Weil height and the canonical height on elliptic curves; Math. Comp.: 1990; Volume 55 ,723-743.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) valuation rings of function fields; coordinate ring of affine; variety over a real closed field; prime cone

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Schubert calculus; Grassmann variety; Schubert cycle; representation of unitary group; intersection numbers

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mori theory; minimal models; Fano variety; Hilbert scheme; rational curves; Chow schemes; vanishing; positive characteristic; Mori's minimal model program; cone theorem; del Pezzo surfaces; Fano varieties Kollár, J., Rational Curves on Algebraic Varieties, (1995), Springer: Springer Berlin

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rationality; Galois group of bitangents; moduli space of plane quartic curves with a flex; Mordell-Weil lattice Shioda, T., Plane quartics and Mordell-Weil lattices of type \(E_7\), Comment. math. univ. st. Pauli, 42, 1, 61-79, (1993)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) birational maps; Cremona group; rational variety Serge Cantat, ``Morphisms between Cremona groups, and characterization of rational varieties'', Compos. Math.150 (2014) no. 7, p. 1107-1124

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Albanese with modulus; relative Chow group with modulus; geometric class field theory Russell, H., \textit{Albanese varieties with modulus over a perfect field}, Algebra Number Theory, 7, 853-892, (2013)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Shafarevich-Tate group; Picard groups; transcendental \(j\)-invariant; finite field; algebraic function field; elliptic curve; fibers of the Néron model; irreducible projective curve; Selmer group; embedding

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Frobenius group; monodromy group; coverings of curves; algebraic function field

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) renormalization; quantum field theory; gauge theory; counterterm; Lagrangian; axiomatic quantum field theory; perturbative quantum field theory; locality axiom; statistical field theory; Wilsonian low energy theory; local action functional; Gel'fand-Fuchs cohomology; continuum quantum field theory; renormalization group flow; effective quantum field theory K.J. Costello, \textit{Renormalisation and Effective Field Theory}, \textit{Mathematical Surveys and Monographs}\textbf{170} (2011), http://bookstore.ams.org/surv-170.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Kummer surface; Jacobian fibrations; Mordell-Weil groups; automorphisms Oguiso K.: On Jacobian fibrations on the Kummer surfaces of the product of non-isogenous elliptic curves. J. Math. Soc. Jpn. 41, 651--680 (1989)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) canonical module; ring of invariants; reductive group; affine variety; generating function Knop, F., Der kanonische modul eines invariantenringes, J. Algebra, 127, 40-54, (1989)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) space of rational maps; action of special linear group; discrete dynamical system; geometric invariant theory Silverman, Joseph H., The space of rational maps on \(\mathbb{P}^1\), Duke Math. J., 94, 1, 41-77, (1998)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic geometry codes of V. D. Goppa; projective curve; finite field; parity-check matrices; rational points; prime divisors of degree 1; algebraic function field

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Behā-Eddīn problem; Mordell-Weil theorem; rational points on elliptic curves Scriba C. J., Zur Geschichte der Bestimmung rationaler Punkte auf elliptischen Kurven: Das Problem von Behā--Eddīn 'Amūlī (1984)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) higher dimensional class field theory; Suslin homology; tame fundamental group

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) function field; bounds for the height of rational points; torsion; canonical height; integral points; elliptic curves

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational torsion point; Jacobian F. Leprévost , Points rationnels de torsion de jacobiennes de certaines courbes de genre 2 , C. R. Acad. Sci. Paris. t. 316 , Série I ( 1993 ), 819 - 821 . MR 1218268 | Zbl 0783.14016

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Riemann surface; moduli space of semistable rank 2 vector bundles; fixed determinant; mapping class group; cohomology class; intersection homology; knot theory Nelson, G., The homology of moduli spaces on a Riemann surface as a representation of the mapping class group, Proc. lond. math. soc. (3), 79, 2, 260-282, (1999)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic modular group; Picard modular group; imaginary quadratic field; K-singular moduli; Hilbert modular group; jacobian; class-numbers of CM-extension Feustel, J, Eine klassenzahlformel für singuläre moduln der picardschen modulgruppen, Comp. Math, 76, 87-100, (1990)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Néron Severi group; Seshadri constant; Jacobian of a hyperelliptic curve; principal polarized abelian variety; theta divisor Steffens A. (1998). Remarks on Seshadri constants. Math. Z. 227: 505--510

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) tropical variety; mixed volume; matroid fan; piece-wise polynomial; intersection theory; toric variety A. Esterov, ''Tropical varieties with polynomial weights and corner loci of piecewise polynomials,'' Mosc. Math. J., 12:1 (2012), 55--76; http://arxiv.org/abs/1012.5800 .

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) quadratic residue curve; Mordell-Weil group

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) transcendence; zero estimates; algebraic independence; Baker's theory; algebraic groups; Neron-Tate height; Abelian variety; exponential function; Weierstrass elliptic function; linear forms in logarithms D. W. Masser, ``Zero estimates on group varieties'' in Proceedings of the International Congress of Mathematicians, Vols. 1-2 (Warsaw, 1983) , PWN, Warsaw, 1984, 493-502.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Veech surfaces; Teichmüller curves; Mordell-Weil group M. Möller, Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve, Invent. Math., 165, 633-649, (2006)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Brauer group; global field; variety; completion Arteche, Giancarlo Lucchini: Le groupe de Brauer non ramifié sur un corps global de caractéristique positive, C. R. Acad. sci. Paris sér. I math. 351, No. 7-8, 299-302 (2013)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) plane curve; finite field; rational point; Frobenius nonclassical curve Homma, M; Kim, SJ, Sziklai's conjecture on the number of points of a plane curve over a finite field III, Finite Fields Appl., 16, 315-319, (2010)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) exceptional Lie group; moduli space over compact Riemann surface; compactification of level set of integrable system; Prym variety; Jacobian variety; completely integrable system Katzarkov, L.; Pantev, T., Stable \(G_2\) bundles and algebraically completely integrable systems, Compos. math., 92, 43-60, (1994)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) topological field theory; topological sigma model; topological-anti-topological fusion; number of vacua and solitons; infrared limit; braid group; \(N = 2\) supersymmetric quantum field theories; helices of coherent sheaves E. Zaslow, ''Solitons and Helices: The Search for a Math-Physics Bridge,'' Commun. Math. Phys. 175(2), 337--375 (1996).

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational points; abelian ramified covers on curves; weil heights on commutative group schemes; Fermat last theorem M. L. BROWN , Endomorphisms of Group Schemes and Rational Points on Curves (Bull. Soc. Math. France, Vol. 115, 1987 , pp. 1-17). Numdam | MR 88h:11040 | Zbl 0628.14017

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) diophantine geometry; arithmetic algebraic geometry; Mordell conjecture; arithmetic Nevanlinna theory; Taniyama-Shimura-Weil conjecture; Heegner points; Arakelov theory; heights; diophantine approximation; Hasse principle; minimal isogenies between 1-motives; integral points; Birch-Swinnerton-Dyer conjecture Lang, S.: Survey of Diophantine geometry. (1997)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Selmer group; Mordell-Weil rank Z. Djabri, Edward F. Schaefer, and N. P. Smart, Computing the \?-Selmer group of an elliptic curve, Trans. Amer. Math. Soc. 352 (2000), no. 12, 5583 -- 5597.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) finite fields; algebraic curves; Riemann-Roch theorem; number of rational points of an algebraic curves over a finite field; Riemann hypothesis; Hasse-Weil bound; asymptotic problems; zeta-functions and linear systems; a characterization of the Suzuki curve; maximal curves; Hermitian curve; Weierstrass points Torres F.: Algebraic curves with many points over finite fields. In: Martínez-Moro, E., Munuera, C., Ruano, D. (eds) Advances in Algebraic Geometry Codes, pp. 221--256. World Scientific Publishing Company, Singapore (2008)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) connected affine algebraic group; finite-dimensional rational representation; normal irreducible affine variety; algebraic subgroup B. Tursunov and Dzh. Khadzhiev, ?Relation between algebras of invariants of an algebraic group and a subgroup of it,? Dokl. Akad. Nauk Uzb. SSR, No. 7, 8?10 (1984).

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Abelian fundamental group; abelian unramified coverings; reciprocity; 0- dimensional Chow group; arithmetical surfaces; unramified class field theory of arithmetical surfaces Kazuya Kato & Shuji Saito, ``Unramified class field theory of arithmetical surfaces'', Ann. Math.118 (1983) no. 2, p. 241-275

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic variety; \(abc\)-conjecture; finiteness theorem for \(S\)-unit points of a diophantine equation; Nevanlinna-Cartan theory over function fields

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) multivariable operator theory; Berezin transform; noncommutative polydomain; noncommutative variety; free holomorphic function; Fock space; invariant subspace; dilation theory; characteristic function G. Popescu, Berezin transforms on noncommutative polydomains, preprint (2013), ; to appear in Trans. Amer. Math. Soc.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) fundamental group; holomorphic action; connected compact complex space; fixed point set; Chow variety

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) character variety; stack; topological field theory; Hodge filtration

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Catalan equation; function field of projective variety; nonconstant solutions; Cassels-Catalan conjecture; Riemann-Hurwitz formula [S] Silverman, J.H.,The Catalan equation over function fields, Trans. A.M.S., 273 (1982), 201--205.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Grothendieck ring for varieties with group actions; motivic zeta-functions; \(K\)-theory; Picard bundle; equivariant bundles; Weil conjectures; invariant theory

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(q\)-deformed geometry; quantum group; motivic zeta function; finite field; braided category; ribbon category

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hasse principle; genus 2; algebraic curves; Jacobian; Mordell-Weil rank Bremner, A.: Some interesting curves of genus 2 to 7. J. Number Theory 67, 277-290 (1997)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curve; Mordell-Weil group

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) undergraduate lecture notes; projective geometry; Grassmannians; intersection theory; Gromov-Witten theory; topological quantum field theory; strings Sheldon Katz, \textit{Enumerative Geometry and String Theory}. Student Mathematical Library, IAS/Park City Mathematical Subseries 32, AMS, Providence 2006.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Zariski pair; Mordell-Weil group; K3 surfaces; complement of plane curves; Milnor index; Alexander polynomials E Artal Bartolo, H Tokunaga, Zariski pairs of index 19 and Mordell-Weil groups of \(K3\) surfaces, Proc. London Math. Soc. \((3)\) 80 (2000) 127

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) cyclicity of group of rational points; sieve theory; primitive root conjecture R. Gupta and M. R. Murty, Cyclicity and generation of points \(\operatorname{mod}p\) on elliptic curves , Invent. Math. 101 (1990), 225-235.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) ACM fat point scheme; complete intersection; fat point scheme; Hilbert function; Kähler different; Kähler differentials; separators

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) group variety; Lehmer's problem; Lang-Silverman conjecture; lower bounds for the height of a point; canonical height; admissible line bundle; Abelian variety; torus Bertrand D., ''Minimal heights and polarizations on group varieties''

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Gysin homomorphisms; localized Chern characters; bivariant intersection theory; commutativity formula; effective Cartier divisors; rational equivalence

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) unramified homomorphisms; descent sequence; isogeny; abelian varieties defined over a number field; Galois cohomological; Selmer group; class field theory; ideal class group

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Severi variety; rational Picard group D. Edidin, Picard groups of Severi varieties, 22 (1994), 2073-2081.