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) modular curve; Hecke algebra; modular deformation; analytic family of modular forms; Mordell-Weil group; modular Jacobian

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 of rational points; Mordell conjecture; trivial subscheme; closed subscheme of an abelian variety M.L. Brown , Remark on two Diophantine conjectures , Bull. London Math. Soc. 17 (1985) 391-392.

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 varieties; finite fields; genus 3; class field theory; curves; rational points; genus 2; Deligne-Lusztig curves; ; Smyth's method; Voloch bound; Ihara constant; Ihara's tower theorem; Golod-Shafarevich theorem; Oesterle's theorem; asymptotic result; explicit formulas Weil's bound

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) Shimura variety; Hasse-Weil zeta function; unitary group; orbital integral Scholze, P., The Langlands-Kottwitz approach for some simple Shimura varieties, Invent. Math., 192, 3, 627-661, (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) algebraic variety; rational points; counting function; complete intersection; non-singular; exponential sum; van der Corput Marmon, O, The density of integral points on complete intersections, Q. J. Math., 59, 29-53, (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) elementary abelian group; complexity; dimension; variety; intersection theory; simple module Carlson, Jon F.: Varieties and modules of small dimension, Arch. math. 60, 425-430 (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) rational points; rank of Mordell-Weil group; invariant of elliptic curve J.-F. Mestre, Rang de courbes elliptiques d'invariant donné, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), 919--922.

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 Dwork cohomology; Katz conjecture; exponential modules; twisted de Rham theory; zeta function of the complete intersection; Weil conjectures; characteristic polynomial; Newton polygon; Hodge polygon; hypersurfaces; middle-dimensional cohomology Adolphson, A.; Sperber, S., On the zeta function of a complete intersection, Ann. Sci École Norm. Sup., 4, 287-328, (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) Fano variety; Picard group; zeta function; height; universal torror; Zariski dense rational points E. Peyre, ''Terme principal de la fonction zêta des hauteurs et torseurs universels,'' in Nombre et Répartition de Points de Hauteur Bornée, , 1998, vol. 251, pp. 259-298.

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 rank at least 19; simple Jacobian; curves of genus 2 Stoll, M., Two simple 2-dimensional abelian varieties defined over \(\mathbb{Q}\) with Mordell-Weil rank at least 19, C. R. Acad. Sci. Paris, Sér. I, 321, 1341-1344, (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) Kolyvagin's descent; Mordell-Weil groups; modular elliptic curve; ring class field extension; Heegner point; Birch and Swinnerton-Dyer conjecture Bertolini, M. and Darmon, H. : Kolyvagin's descent and Mordell-Weil groups over ring class fields , J. für die Reine und Angewandte Mathematik 412 (1990), 63-74.

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) distance function; variety over a complete nonarchimedean field; approximation by 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) Mordell-Weil group; Jacobian; Galois conjugates

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) elementary equivalence; isomorphism; isogeny; function field; Severi-Brauer variety; quadric; elliptic curve; Jacobian

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; ramification of division points; non-existence of abelian variety of type (K); Néron model; class number

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) Aubry-Perret bound; finite field; Hasse-Weil bound; rational function

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 function field; quadratic number field; ideal class group; algorithm; Jacobian; hyperelliptic curve; concordant ideals; g-adic numbers; elliptic function fields; elliptic curves; 2-descent Hellegouarch, Y.: Algorithme pour calculer LES puissances successives d'une classe d'idéaux dans uns corps quadratique. Application aux courbes elliptiques. C. R. Acad. sci. Paris sér. I 305, 573-576 (1987)

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; Jacobians; curves of higher genus; descent; 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) quadratic form; Springer's theorem; Brauer group; Witt kernel; Pfister form; field extension; hyperelliptic curve; affine hypersurface; rational point

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; rational 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) algebraic function field; rational function field; dihedral group; discriminant; zeta-function; divisor class number; ideal class number

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 surface; finite field; rational point; abelian 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) algebraic curve; finite field; rational point; zeta function Y. Aubry and M. Perret, \textit{On the characteristic polynomials of the Frobenius endomorphism for projective curves over finite fields}, Finite Fields Appl., 10 (2004), pp. 412--431.

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) Tate-Shafarevich group; Mordell-Weil theorem; descent; elliptic Iwasawa theory; Selmer group; survey; Birch-Swinnerton-Dyer conjecture

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; Néron-Severi group; Jacobian variety; Néron-Tate pairing; number of fixed points; Thue curves; number of integral 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) Chabauty; Coleman; Jacobian; divisor; abelian integral; Mordell-Weil sieve; generalized Fermat; rational points Siksek S., Explicit Chabauty over number fields, Algebra Number Theory 7 (2013), no. 4, 765-793.

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) multiplicity of a root of an algebraic equation; multiplicity of a point of an algebraic variety; intersection multiplicity of algebraic varieties at a point; Weil's multiplicity; Hilbert-Samuel's multiplicity

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) Selmer group; Jacobian; bound for the Mordell-Weil rank; elliptic curves Stoll, M.: On the arithmetic of the curves y2=x\(\ell +A\) and their Jacobians. J. reine angew. Math. 501, 171-189 (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) Picard group; Tamagawa number; Brauer-Manin obstruction; Zbl 0991.72285; asymptotic behaviour; counting function; number of rational points of bounded height; Fano variety; geometric invariants; diagonal cubic surfaces; algorithm Peyre, E.; Tschinkel, Y., \textit{Tamagawa numbers of diagonal cubic surfaces, numerical evidence}, Math. Comp., 70, 367-387, (2001)

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) Chow group; intersection theory; coarse moduli space; Q-variety; algebraic stack; Riemann-Roch Gillet, Henri, Intersection theory on algebraic stacks and {\(Q\)}-varietiesproceedings of the {L}uminy conference on algebraic {\(K\)}-theory, J. Pure Appl. Algebra, 34, 193-240, (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) rational points; transcendental points; arithmetically generic point; height; analytic Riemann surface; algebraic variety; arithmetic polarization; algebraic foliation by curves; Liouville inequality; Nevanlinna theory; arithmetic geometry; Arakelov 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) intersection theory; Mordell conjecture; Chow group A. J. de Jong, ``Ample line bundles and intersection theory'' in Diophantine Approximation and Abelian Varieties (Soesterberg, Netherlands, 1992) , ed. B. Edixhoven and J.-H. Evertse, Lecture Notes in Math. 1566 , Springer, Berlin, 1993, 69--76.

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 ground field; hyperelliptic Jacobian; endomorphisms of abelian variety; unitary group; Hermitean group; Galois group; Steinberg representation Zarhin Yu.G. (2003). Hyperelliptic jacobians and simple groups U3(2 m ). Proc. AMS 131: 95--102

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-linear endomorphism of De Rham cohomology group; Jacobian of the Fermat curve; crystalline Weil group; Frobenius matrices; Morita gamma function R. Coleman, On the Frobenius matrices of Fermat curves, \textit{p}-adic analysis, Lecture Notes in Math. 1454, Springer, Berlin (1990), 173-193.

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 surfaces; elliptic curves over function fields; generators of Mordell-Weil group; Kodaira-Néron model; number of minimal sections; specialization homomorphisms

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 cover; Cremona group; rational elliptic surface; Mordell-Weil group; birational 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) Kronecker's Jugendtraum; elliptic functions; elliptic integrals; arithmetic of elliptic curves; Weierstrass \(\wp\)-function; projective plane cubics; Abel's theorem; inversion problem; Jacobi functions; theta functions; Lefschetz theorem; embeddings; theta identities; Euler identities; Jacobi substitutions; quadratic reciprocity; Siegel modular group; modular forms; Eisenstein series; modular equation; arithmetic subgroups; arithmetic applications; solvability of algebraic equations; Galois theory; Klein's icosaeder; quintic equation; imaginary quadratic number fields; class invariants; class polynomial; Mordell-Weil theorem Henry McKean and Victor Moll, \textit{Elliptic Curves}, Cambridge University Press, Cambridge, 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) multiplicative structure; skew fields over number fields; Hasse; norm principle; algebraic group; group of rational points; quadratic forms; Skolem-Noether theorem; algebra of quaternions; class field theory; direct subgroup; Spin(f); SL(1,D); trace Platonov V P and Rapinchuk A S, Proceedings of Steklov Institute of Math. 1985, Issue 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) rational elliptic surfaces; Mordell-Weil group; Zariski \(N\)-plets

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 of homogeneous space; level of a field; equivariant cohomology; real abelian variety; Picard group Van Hamel, J., \textit{divisors on real algebraic varieties without real points}, Manuscripta Math., 98, 409-424, (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) Complex multiplication of abelian varieties; total imaginary quadratic extension of totally real field; class field theory; Frobenius endomorphism; zeta function of abelian variety; Hilbert's 12th problem Shimura, G. and Taniyama, Y. Complex multiplication of abelian varieties and its applications to number theory The Mathematical Society of Japan, Tokyo, 1961 Math Reviews MR0125113 (23 \#A2419)

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; automorphism group of a curve Keel, S., M\(^{\mathrm c}\)Kernan, J.: Rational Curves on Quasi-Projective Surfaces. Memoirs of the American Mathematical Society, vol. 140(669). American Mathematical Society, Providence (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) coverings of \(\mathbb{P}^ 1\); Galois groups; Hurwitz monodromy group; finite groups; Galois group of regular extension of \(\mathbb{Q}\); universal Frattini cover; rational point on varieties; regular realization problem on dihedral groups; real branch points; totally nonsplit extension; field of totally real numbers; fields of definition; inverse Galois problem; symmetric group; modular curves Dèbes, Pierre; Fried, Michael D., Nonrigid constructions in Galois theory, Pacific J. math., 163, 1, 81-122, (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) Calabi-Yau threefolds; rational points; Mordell-Weil group; Néron model

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) curve; rational point; zeta function; Weil bound; Serre bound; Oesterlé bound Howe, E., Lauter, K.: Improved upper bounds for the number of points on curves over finite fields. Ann. Inst. Fourier~53, 1677--1737 (2003); corrigendum to: Improved upper bounds for the number of points on curves over finite fields. Ann. Inst. Fourier (Grenoble) 57(3), 1019--1021 (2007)

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) \(\mathbb Q\)-factoriality; complete intersection; Noether-Halphen theory; Weil divisor class group C. Ciliberto and V. Di Gennaro, Factoriality of certain hypersurfaces of \(\mathbf{P}^{4}\) with ordinary double points , Algebraic transformation groups and algebraic varieties, Encyclopaedia Math. Sci., 132, pp. 1-7, Springer, Berlin, 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) quartic Diophantine equations; computation of Selmer group; Jacobian of a curve; algorithms; Mordell-Weil ranks E. Schaefer, ''Computing a Selmer Group of a Jacobian Using Functions on the Curve,'' Math. Ann. 310, 447--471 (1998); ''Erratum,'' Math. Ann. 339, 1 (2007).

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; local field; Langlands conjectures; irreducible representations; Weil-Deligne group; Iwahori subgroup; equivariant K- homology; K-theory of coherent sheaves George Lusztig, Representations of affine Hecke algebras, Astérisque 171-172 (1989), 73 -- 84. Orbites unipotentes et représentations, II.

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) inverse problem of Galois theory; Fischer-Griess monster as Galois group over \({\mathbb{Q}}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_ 2({\mathbb{R}})\); congruence subgroup; modular curve; Puiseux-series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps; lectures

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; torsion group; field of rational numbers; generator (basis point); short Weierstraß\ form Qiu, D., Zhang, X.: Explicit classification for torsion subgroups of rational points of elliptic curves. Acta Math. Appl. Sinica (English Ser.) 18, 539--548 (2002)

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) complex multipliction; isogenous Jacobian; real multiplication; rational function field; hyperelliptic curves Mestre, J. F.: Courbes hyperelliptiques à multiplications réelles. C. R. Acad. sci. Paris, ser. I math. 307, 721-724 (1988)

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 rank; Néron-Severi group; basis for the group of rational points; elliptic surface; computer calculation; height functions Kuwata, M., The canonical height and elliptic surfaces, J. Number Theory, 36, 2, 201-211, (1990), MR 1072465

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; Mordell-Weil; variety; 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) upper bounds for solutions of diophantine equations; Runge theorem; finiteness of number of solutions; Brauer-Siegel theorem; Baker-Coates theory; linear forms in logarithms of algebraic numbers; \(p\)-adic case; representation of numbers by binary forms; Thue equation; rational approximations to algebraic numbers; effective strengthening of Liouville inequality; solution of Thue equation in \(S\)-integers; non-Archimedean metrics; polynomial equation; Mordell equation; Catalan equation; size of ideal class group; small regulator; effective variants of Hilbert on irreducibility of polynomials; Abelian points on algebraic curves Sprindžuk, Vladimir G., Classical Diophantine Equations, Lecture Notes in Mathematics 1559, xii+228 pp., (1993), Springer-Verlag, 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) Jacobian; genus four curves; universal family; Mordell-Weil group; Franchetta's conjecture

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) inverse problem of Galois theory; Fischer-Griess monster as Galois group over \(\mathbb{Q}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_2(\mathbb{R})\); congruence subgroup; modular curve; Puiseux series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps J. Thompson , Some finite groups which appear as Gal (L/K) where K \subset Q(\mu n) , J. Alg. 89 (1984) 437-499.

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) hyperelliptic curve; Weierstrass point; Selmer group; Mordell-Weil group Benedict H. Gross, Hanoi lectures on the arithmetic of hyperelliptic curves, Acta Math. Vietnam. 37 (2012), no. 4, 579 -- 588.

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) mirror symmetry; mirror map; complete intersection Calabi-Yau spaces; Picard-Fuchs equations; instanton corrected Yukawa couplings; topological oneloop partition function; higher dimensional moduli spaces; closed formulas; prepotential; Kä|hler moduli fields; singular ambient space; nonsigular weighted projective spaces; three generation models; topology change; local solutions; topological invariants; Calabi-Yau manifold; rational superconformal field theories; elliptic curves; \(E_6\) gauge couplings; \(E_8\) gauge couplings; threshold corrections; Gromov-Witten invariants S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, \textit{Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces}, \textit{Nucl. Phys.}\textbf{B 433} (1995) 501 [hep-th/9406055] [INSPIRE].

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) Virasoro conformal blocks; Painlevé transcendents; Stokes matrices; Stokes sectors; monodromy; Riemann-Hilbert problem (RHP); Fredholm determinant; Whittaker functions; Szegő constant; Toeplitz determinant; Young diagrams; Ponsot-Teschner Formula; quantum dilogarithms; connection formulas; connection constants; regular conformal blocks; irregular conformal blocks; Alday-Gaiotto-Tachikawa (AGT) relation; conformal field theory (CFT); 4D supersymmetric gauge theory; Nekrasov functions; Whittaker vectors; Whittaker module; Virasoro generators; Weyl symmetry group; Chiral vertex operator; tau function; Lax pair; Jimbo-Miwa-Ueno tau function; connection problem; Barnes \(G\)-function; Verma module; Virasoro algebra Lisovyy, O.; Nagoya, H.; Roussillon, J., Irregular conformal blocks and connection formulae for Painlevé V functions, J. Math. Phys., 59, 091409, (2018)

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) invariant field of automorphism group; rational function field; rationality problem

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 over global fields; Mordell-Weil group; twist theory Yamagishi, H, On certain twisted families of elliptic curves of rank 8, Manuscr. Math., 95, 1-10, (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 curve; finite field; linear code; zeta function; moduli space; Jacobian variety van der Geer G.: Coding theory and algebraic curves over finite fields: a survey and questions. In: Applications of Algebraic Geometry to Coding Theory, Physics and Computation, NATO Sci. Ser. II Math. Phys. Chem., vol. 36, pp. 139--159. Kluwer, Dordrecht (2001).

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 of rational points; finite field; Newton polygon; Hodge polygon Rybakov, S., On classification of groups of points on abelian varieties over finite fields, Mosc. Math. J., 15, 4, 805-815, (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) reciprocity law for surfaces over finite fields; group of degree 0 zero- cycles; rational equivalence; abelian geometric fundamental group; unramified class field theory; K-theory; Chow groups Jean-Louis Colliot-Thélène & Wayne Raskind, ``On the reciprocity law for surfaces over finite fields'', J. Fac. Sci. Univ. Tokyo Sect. IA Math.33 (1986) no. 2, p. 283-294

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) hypersurface; rational point; finite field; Veronese variety; Reed-Muller code; generalized Hamming weight Datta, M.; Ghorpade, S. R., On a conjecture of tsfasman and an inequality of Serre for the number of points of hypersurfaces over finite fields, Mosc. Math. J., 15, 4, 715-725, (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) \(l\)-adic Abel-Jacobi map; group of codimension-\(n\) cycles modulo rational equivalence; filtration; \(l\)-adic étale cohomology; cycle map; function field in one variable W. Raskind, ''Higher \(l\)-adic Abel-Jacobi mappings and filtrations on Chow groups,'' Duke Math. J., vol. 78, iss. 1, pp. 33-57, 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) Brauer group; rational function field; ABF theorem

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) narrow Mordell-Weil lattice; group of rational points on an elliptic curve; Weyl groups as Galois groups; sphere packing; algebraic equations; inverse Galois problem; Kodaira-Néron model; height pairing; Néron- Severi group; rational elliptic surface

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) transfer principle; absolute Galois group of the rational function field; real closed field; Tarski principle L. van den Dries and P. Ribenboim, ''An application of Tarski's principle to absolute Galois groups of function fields,'' Ann. Pure Appl. Log., 33, 83--107 (1987).

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; rational points; Mordell-Weil group; generator; canonical height; local height

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) curves over global fields; Jacobian; 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) elliptic curves over function fields; Mordell-Weil rank; Néron-Tate regulator; Tate-Shafarevich group; \(L\)-function; BSD conjecture

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; Iwasawa theory; \(p\)-adic heights; \(p\)-adic \(L\)-function; height pairing of abelian varieties; Iwasawa function; rational point of infinite order; Tate duality Karl Rubin, Abelian varieties, \?-adic heights and derivatives, Algebra and number theory (Essen, 1992) de Gruyter, Berlin, 1994, pp. 247 -- 266.

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) isotriviality; effective Mordell; semiabelian variety; positive characteristic; survey of diophantine geometry; bounding the heights of rational points on curves over function fields; semiabelian varieties; Roth's theorem Voloch, José Felipe, Diophantine geometry in characteristic \(p\): a survey.Arithmetic geometry, Cortona, 1994, Sympos. Math., XXXVII, 260-278, (1997), Cambridge Univ. Press, Cambridge

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 variety; isogeny; theta group; theta function; discrete logarithm problem; non-hyperelliptic 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) elliptic curves; generators; group of rational points; Mordell-Weil lattice invariant H. E. Rose, On a class of elliptic curves with rank at most two, Math. Comp. 64 (1995), no. 211, 1251 -- 1265, S27 -- S34.

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 over a global function field; Mordell-Weil lattices; determinants; cycle-class map; crystalline cohomology; height pairing [3] N. Dummigan, `` The determinants of certain Mordell-Weil lattices {'', \(Amer. J. Math.\)117 (1995), no. 6, p. 1409-1429. &MR 13 | &Zbl 0914.}

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) analytic Hilbert quotient; momentum map; G-variety; semistability; complex reductive Lie group; good quotient; Weil divisor; geometric invariant theory (GIT) Greb, D, Compact Kähler quotients of algebraic varieties and geometric invariant theory, Adv. Math., 224, 401-431, (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) 2-Selmer group; hyperelliptic curve; function field; Jacobian

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) \(n\)-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)

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; Weil bound; maximal variety; classification of surfaces; Betti numbers; finite field; Drinfeld-Vladut bound M. A. Tsfasman, ''Nombre de points des surfaces sur un corps fini,'' in Arithmetic, Geometry, and Coding Theory, Luminy, 1993 (Walter de Gruyter, Berlin, 1996), pp. 209--224.

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) intersection number of two divisors; normal surface; bivariant intersection theory; Chow group; rational equivalence; algebraic equivalence S. Kimura, Fractional intersection and bivariant theory, Comm. Algebra 20 (1992), no. 1, 285-302.

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) projective variety; Chow group; rational point; Witt-rational singularity

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) rigid analysis; Picard variety; rational point; formal model; Picard functor; Poincaré line bundle; Néron-Severi group U. Hartl and W. Lütkebohmert, On rigid-analytic Picard varieties, J. reine angew. Math. 528 (2000), 101-148.

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) absolute Galois group of rational function field; real closed field; Tarski principle; transfer principle L P.D. v.d. Dries and P. Ribenboim , An application of Tarski's principle to absolute Galois groups of function fields , Queen's Mathematical Preprint No. 1984-8.

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 curve; Jacobian; Mordell-Weil group; real hyperelliptic 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) elliptic curve; Mordell-Weil group; generators; height function

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 field; connected reductive linear group; Weyl discriminant; invariant distribution; rational function; GL(n); poles; orbital integrals; Shalika germs

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) global function fields; rational places; rational points; curves over finite fields; class field towers; applications to coding theory; low-discrepancy sequences Niederreiter, Harald; Xing, Chaoping: Rational points on curves over finite fields--theory and applications, (2000)

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) norm group; birational invariant; complete variety; function field Rost, M.: Durch Normengruppen definierte birationale Invarianten. C. R. Acad. Sci. Paris Sér. I, Mathématiques. 310, 189-192 (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) Deligne-Lusztig variety; zeta function; Betti numbers; rational points; Weil-Deligne bound Rodier, F., Nombre de points de surfaces de Deligne--Lusztig, C. R. Acad. Sci. Paris Sér. I Math., 322, 6, 563-566, (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) Hasse-Weil bound; rational point; Weierstrass point; minimal curve; gap; genus; zeta function Viana, PH; Rodriguez, JEA, Eventually minimal curves, Bull. Braz. Math. Soc, 36, 39-58, (2005)

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) moduli space of vector bundles; representation spaces; fundamental group; Seifert manifold; \({\mathbb{Z}}\)-homology sphere; Floer homology; Morse function; Dolgachev surface; Chern classes; smooth rational varieties; Betti numbers; Weil conjectures S. Bauer and C. Okonek, The algebraic geometry of representation spaces associated to Seifert fibered homology \(3\)-spheres , Math. Ann. 286 (1990), no. 1-3, 45-76.

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; complex multiplication; Mordell-Weil group; Tate- Shafarevich group; Iwasawa theory Rubin, Karl, Elliptic curves and \({\mathbf Z}_p\)-extensions, Compositio Math., 0010-437X, 56, 2, 237-250, (1985)

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 of rational points; cyclic; abelian variety; finite 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) function field analogue of the theory of elliptic modular curves; Drinfeld modules; Drinfeld's upper half-plane; expansions at the cusps of certain modular forms; Manin-Drinfeld theorem; algebraic modular forms; jacobian Ernst-Ulrich Gekeler, Drinfel\(^{\prime}\)d modular curves, Lecture Notes in Mathematics, vol. 1231, Springer-Verlag, Berlin, 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) Siegel modular group; resolution of cusps; rational Hilbert modular surfaces; canonical maps; modular curves; intersection theory; moduli spaces; abelian varieties with real multiplication; Kummer surface Friedrich Hirzebruch and Gerard van der Geer, Lectures on Hilbert modular surfaces, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 77, Presses de l'Université de Montréal, Montreal, Que., 1981. Based on notes taken by W. Hausmann and F. J. Koll.

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) effective Chabauty; cardinality of rational points on a curve; Fermat's Last Theorem; rank of the Mordell-Weil group; Fermat curve; rational points on curves W. G. McCallum, ''On the method of Coleman and Chabauty,'' Math. Ann., vol. 299, iss. 3, pp. 565-596, 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) elliptic curve with complex multiplication; Mordell-Weil group; p-adic height function D. Bertrand, Relations d'orthogonalité sur les groupes de Mordell-Weil , Séminaire de théorie des nombres, Paris 1984-85, Progr. Math., vol. 63, Birkhäuser Boston, Boston, MA, 1986, pp. 33-39.

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) 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.