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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) number of rational points; genus; Jacobian; Mordell-Weil rank; Chabauty's theorem Grant, D.: A curve for which Coleman's Chabauty bound is sharp. Preprint, 1991

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; multiplicative invariants; inverse Galois problem; Weyl group; Mordell-Weil group Kumar, Abhinav; Shioda, Tetsuji, Multiplicative excellent families of elliptic surfaces of type \(E_7\) or \(E_8\), Algebra Number Theory, 1937-0652, 7, 7, 1613-1641, (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) manifold; singular variety; vector field; obstruction theory; Chern-Weil theory; Baum-Bott residue; singular foliation; Camacho-Sad index; Chern class; Euler class; Euler-Poincaré characteristic; Fulton-Johnson class; Grothendieck residue; GSV index; homological index; MacPherson class; Mather class; Milnor class; Milnor number; Thom class; Nash bundle; Poincaré-Hopf index; Schwartz index; Schwartz-MacPherson class; virtual index Brasselet, J.-P., Seade, J., and Suwa, T., \textit{Vector fields on singular varieties}, Lecture Notes in Mathematics, vol. 1987, Springer-Verlag, Berlin, 2009.

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) higher degree diophantine equations; rational points; Fermat curve; Jacobian; Mordell-Weil theorem; torsion

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 measure; p-adic interpolation of special values of Hecke L- functions; elliptic curve over an imaginary quadratic field; complex multiplication; rank of the 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) curve; finite field; Jacobian; abelian variety; Fermat curve; Frobenius; verschiebung; group scheme; de Rham cohomology; Dieudonné module; \(p\)-divisible 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) group of rational points; Mordell-Weil group; Jacobians; arithmetic of hyperelliptic curves; 2-descent; points of bounded height E. F. Flynn, ''The arithmetic of hyperelliptic curves,'' in: Algorithms in Algebraic Geometry and Applications, Progress Math., Vol. 143, Birkhäuser, Boston (1996), pp. 165--175.

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; rational surfaces; Mordell-Weil group C. Salgado, Construction of linear pencils of cubics with Mordell-Weil rank five, Comment. Math. Univ. St. Pauli, 58 (2009), 95-104.

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; order of the torsion part of the Mordell-Weil group; Jacobian; Eisenstein quotient Edixhoven, B.: Rational torsion points on elliptic curves over number fields (after kamienny and Mazur). Astérisque 227, 209-227 (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) abelian variety over a finite field; deterministic algorithm; characteristic polynomial of the Frobenius endomorphism; Jacobian varieties; rational points; hyperelliptic curves; primality test; complexity analysis L.M. Adleman and M.-D. Huang, Counting rational points on curves and Abelian varieties over finite fields , %in Algorithmic number theory ANTS-II, Lect. Notes Comp. Sci. 1122 (1996), 1-16%, Berlin (Germany), 1996.%Springer-Verlag.

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; sphere packing; algebraic equations; inverse Galois problem; group of rational points on an elliptic curve; Kodaira- Néron model; height pairing; Néron-Severi group; rational elliptic surface; Weyl groups as Galois groups : Theory of Mordell-Weil lattices, Proc. ICM Kyoto 1990, vol. I, (1991) 473--489

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; projective curve; obstruction to the Hasse principle; conic bundles; rational point Antoine Ducros, L'obstruction de réciprocité à l'existence de points rationnels pour certaines variétés sur le corps des fonctions d'une courbe réelle, J. Reine Angew. Math. 504 (1998), 73 -- 114 (French, with English summary).

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) variety over a finite field; Tate's conjectures; Picard number; Brauer group; Néron-Severi group; special values of the zeta function Suwa, Noriyuki and Yui, Noriko, Arithmetic of certain algebraic surfaces over finite fields, Number Theory ({N}ew {Y}ork, 1985/1988), Lecture Notes in Math., 1383, 186-256, (1989), 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) elliptic surface; rational elliptic surface; automorphism group; Mordell-Weil group; \(J\) map Karayayla, T., Automorphism groups of rational elliptic surfaces with section and constant \(J\)-map, Cent. eur. J. math., 12, 12, 1772-1795, (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) witness set; generic point; homotopy continuation; cascade homotopy; irreducible component; multiplicity; numerical algebraic geometry; polynomial system; numerical irreducible decomposition; primary decomposition; algebraic set; algebraic variety; number field; Galois 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) pseudo real closed field; prc-fields; rational point; absolute Galois 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) monodromy transformation; complete valuated field; rational point; characteristic polynomial of an automorphism of a curve; first homological group Lorenzini, D., The characteristic polynomial of a monodromy transofmration attached to a family of curves, Comm. Math. Helvetici, 68, 111-137, (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) lattice polytope; reflexive polytope; lattice point enumeration; Ehrhart polynomial; rational generating function; Betti number; Gorenstein toric variety Mustaţǎ, Mircea; Payne, Sam, Ehrhart polynomials and stringy Betti numbers, Math. Ann., 333, 4, 787-795, (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) finite field; algebraic variety; rational point; degree matrix

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; constructing elliptic curves with high rank; rational points; Mordell-Weil-lattices; invariant of the Weyl groups; universal deformation of the rational double point; \(E_ 8\); root lattices T. Shioda, Construction of elliptic curves with high-rank via the invariants of the Weyl groups, J. Math. Soc. Japan43 (1991) p.673--719.

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) Fermat septic; quotient of Fermat curves; Mordell-Weil group of the 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) constructive Galois theory; fundamental group; field of definition; ramification structures; topological automorphisms; algebraic; function field; \(PSL_ 2({\mathbb{F}}_ p)\) Matzat, B.H.: Topologische Automorphismen in der konstruktiven Galoistheorie. Erscheint demnächst

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; ordinary abelian variety; finite field; isogeny class; class of matrices

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) density of rational points; function field analogue of the generalized Mordell conjecture K. MAEHARA, On the higher dimensional Mordell conjecture over function fields, Osaka J. Math. 2 (1991), 255-261.

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 algebraic curves; topological quantum field; Fano varieties; Gromov-Witten classes; complex projective algebraic manifold; quantum cohomology; Weil-Petersson volume forms; topological intersection formula M. Kontsevich and Yu. Manin, Quantum cohomology of a product, With an appendix by R. Kaufmann, \doihref10.1007/s002220050055Invent. Math., 124 (1996), 313--339.

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) field of definition for the Mordell-Weil group; ramification of field extension; elliptic curve; configuration of the points of bad fibers

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 lattice; splitting field; explicit generators of rational points Shioda, T., The Mordell-Weil lattice of \(y^2 = x^3 + t^5 - 1 / t^5 - 11\), Comment. Math. Univ. St. Pauli, 56, 1, 45-70, (2007), MR 2356749

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) zeta function; quantum statistical mechanical system; abelian class field theory; Galois group G. Cornelissen and M. Marcolli, ''Quantum statistical mechanics, L-series and anabelian geometry,'' [arXiv:1009.0736].

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; Mordell-Weil group; absolutely simple Jacobian 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) survey; intersection homology; Poincaré duality; singular spaces; Morse theory; fixed point indices; \(L^ 2\)-cohomology; intersection homology sheaf; specialization; Weyl group representations; Hecke algebras, representations of Lie algebras Robert MacPherson, Global questions in the topology of singular spaces, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 213 -- 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) cubic surface; Schläfli-Cayley classification; quasi-group; Mordell-Weil group; finite field; Suslin homology

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 law on the Jacobian of a curve of genus 2; Mordell-Weil rank -, Arithmetic of curves of genus \( 2\), Number Theory and Applications , Kluwer, 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) Bibliography; computer algebra systems; Gröbner bases; ideal membership; Hilbert function; elimination; Milnor numbers; Beilinson monads; \(D\)-modules; primary decomposition; normalization; Puiseux expansion; rational parametrization; deformations; invariant rings; special varieties; intersection theory; syzygy conjectures; Zariski's conjecture; visualisation; complexity

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; cryptosystems; discrete logarithm; group of rational points; elliptic curve over a finite field; practical implementations; algorithms; running times R. Harasawa, J. Shikata, J. Suzuki, H. Imai, Comparing the MOV and FR reductions in elliptic curve cryptography, in: Advances in Cryptology--Eurocrypt '99, Lecture Notes in Computer Science, Vol. 1592, Springer, Berlin, 1999, pp. 190--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) root systems; connected reductive algebraic group; projective variety; Borel subgroups; line bundles; orbits; tangent bundle; Weyl group; maximal tori; \(\ell\)-adic cohomology groups; virtual representation; characters; irreducible representations; multiplicities; irreducible components; intersection cohomology; Schubert cells; Weyl groups; Hecke algebras; enveloping algebras; complex reductive Lie algebras; unipotent representations G. Lusztig. Characters of reductive groups over a finite field, Ann. Math. Studies 107, Princeton University Press, 1984. ''BN13N22'' -- 2018/1/30 -- 14:57 -- page 225 -- #27 2018] QUANTIZATIONS OF REGULAR FUNCTIONS ON NILPOTENT ORBITS 225

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) arithmetic site; monoid; topos; topos automorphism; Adele ring; topos-theoretic point; torsion-free abelian group; zeta function; Goormaghtigh 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) group of rational points; reductive connected algebraic group; irreducible characters; unipotent elements; class functions; orthonormal bases; characteristic functions; irreducible perverse sheaves; character sheaves; local intersection cohomology; principal series representation; Green functions; unipotent representations Lusztig, G.: On the character values of finite Chevalley groups at unipotent element. J. Algebra,104, 146--194 (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) rational points of algebraic curves; theorem of Mordell-Weil; effectivity; Diophantine approximation [9] J. Cassels, \(Mordell's finite basis theorem revisited\). Math. Proc. of the Cambridge Phil. Soc. 100 (1986), 31-41. &MR 8 | &Zbl 0601.

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 positive characteristic; arithmetic fundamental group; Galois representation; automorphic representation G. Böckle and C. Khare, Finiteness results for mod \(l\) Galois representations 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) Hasse-Weil-Serre bound; zeta function of curves over finite fields; rational points K. Lauter, Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields, Institut de Mathématiques de Luminy, preprint, 1999, pp. 99--29.

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; function field; anabelian geometry Szamuely, T., Groupes de Galois de corps de type fini (d'après pop), Astérisque, 294, 403-431, (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) Frobenius manifolds; cohomological field theory; commutativity equation; Losev-Manin compactification; Givental's group action; Kadomtsev-Petviashvili hierarchy Shadrin, S., Zvonkine, D.: A group action on Losev--Manin cohomological field theories. arXiv:0909.0800v1, 1--21

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; variety; genus; singularity; dimension; rational function; tangent space; surface; birational equivalence Reid, M.: Undergraduate algebraic geometry. London mathematical society student texts (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) Brauer groups of fields of invariants; Galois cohomology; Artin-Mumford group of the field of rational functions Bogomolov F.A., Brauer groups of fields of invariants of algebraic groups, Math. USSR-Sb., 1990, 66(1), 285--299

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; Hasse-Witt invariants; Deuring-Shafarevich formula; Galois group; maximal unramified p-extension; p-profinite completion

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) Demazure models; fan; action of the Galois group; complete variety over a nonclosed 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) real algebraic geometry; real algebraic varieties; complexification; Smith's theory; Galois-Maximal varieties; algebraic cycles; real algebraic models; algebraic curves; algebraic surfaces; topology of algebraic varieties; regular maps; rational maps; singularities; algebraic approximation; Comessatti theorem; Rokhlin theorem; Nash conjecture; Hilbert's XVI problem; Cremona group; real fake planes

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) arithmetic function; number of factorizations of an integer; group of rational 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) generalization of class field theory; local fields; Milnor K-group; integral projective scheme; Chow group; generalization of ramification theory; higher dimensional schemes; generalized Swan conductor; global 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) brief survey; Mordell-Weil group; 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 simplicial polytope; fixed-point free linear symmetry; Cohen- Macaulay complex; \(h\)-vector; toric variety Adin, R.M., On \textit{h}-vectors and symmetry, (Jerusalem combinatorics '93, Contemp. math., vol. 178, (1994), Amer. Math. Soc. Providence, RI), 1-20, MR 1310571 (96e:52029)

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) extremal elliptic K3 surface; Picard number; 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) Arakelov varieties; \(\Theta\)-divisor; Jacobian; arithmetic varieties; height functions; arithmetic intersection 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) del Pezzo surface; finite field; rational point

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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; Drinfeld modules over the rational function field; Galois representation; supersingular reductions Poonen, B., Drinfeld modules with no supersingular primes, Int. Math. Res. Not. IMRN, 3, 151-159, (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) rational points; finite field; hypergeometric function Salerno, Adriana, Counting points over finite fields and hypergeometric functions, Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydział\ Matematyki i Informatyki. Functiones et Approximatio Commentarii Mathematici, 49, 1, 137-157, (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) trace of monodromy; geometric Frobenius; finite residue field; Weil group Ochiai, T., \textit{ \textit{l}-independence of the trace of monodromy}, Math. Ann., 315, 321-340, (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) local-global principle; rational points; Weil-Châtelet group; elliptic curves

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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 group; algebraic variety; action; rational quotient 10.1007/s40879-015-0050-8

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) affine algebra varieties; quasiprojective varieties; intersection theory; birational equivalence; algebraic groups; degenerations; Bertini theorems; singularities; zeta function I.~Shafarevich. \textit{Basic algebraic geometry~1: varieties in projective space}, 2nd edition, Springer, Berlin 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) zeta-function; number-field; finiteness of Brauer group; function-field analogue of the conjecture of Birch and Swinnerton-Dyer Lichtenbaum, S.: Behavior of the zeta-function of open surfaces at s=1. Adv. stud. Pure math. 17, 271-287 (1989)

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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) enumerative geometry; intersection theory; multiple-point theory; Hilbert schemes; quadrics; cubics Kleiman, S. L.: Intersection theory and enumerative geometry: a decade in review. Proc. Symp. Pure Math.46, 321--370 (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 1-form; locally analytic function; abelian variety; \(p\)-adic period; Frobenius operator; \(p\)-adic polylogarithm; Coleman integration; Colmez integration

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) Weil numbers; smooth curve over a field; zeta function; Riemann hypothesis; abelian varieties over finite fields Rück, H. G., Abelian surfaces and Jacobian varieties over finite fields, Compos. Math., 76, 3, 351-366, (1990)

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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 residue; two dimensional irreducible complex representation; cusp form of weight one; Weil-Langlands theory; Fourier coefficients; identities between cusp forms; quartic reciprocity; higher reciprocity law; cusp form of weight two; inverse Mellin transform; L-function of elliptic curve; congruence mod 4 N. Ishii, ''Cusp forms of weight one, quadratic reciprocity and elliptic curves,''Nagoya Math. J.,98, 117--137 (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) unramified homomorphisms; descent sequence; isogeny; abelian varieties defined over a number field; Galois cohomological; Selmer group; class field theory; ideal class group Schaefer E.\ F., Class groups and Selmer groups, J. Number Theory 56 (1996), no. 1, 79-114.

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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 number of generators; variety of characters of \(n\)-dimensional representations; group of finite width; arithmetic subgroups; algebraic number field; simply connected algebraic group; Zariski-dense \(S\)- arithmetic subgroup; subgroups of finite index Rapinchuk, A. S.: Representations of groups of finite width. Dokl. akad. Nauk SSSR 315, 536-540 (1990)

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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 rank; Selmer group; Jacobians; curves over global fields; Shafarevich--Tate group; descent; Galois cohomology B. Poonen and E. Schaefer, ''Explicit Descent for Jacobians of Cyclic Covers of the Projective Line,'' J. Reine Angew. Math. 488, 141--188 (1997).

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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) dimension of real algebraic homology group; real algebraic variety; Zariski closed real algebraic hypersurfaces; Albanese variety; endomorphisms; complex elliptic curve; jacobian variety Bochnak J., Kucharz W.: Real algebraic hypersurfaces in complex projective varieties. Math. Ann. 301, 381--397 (1995)

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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) limit linear series; higher Picard group; higher Jacobian; complex curve; isomorphism classes of line bundles of degree \(d\); Albanese variety; moduli space of pointed curves Ciro Ciliberto, Joe Harris, and Montserrat Teixidor i Bigas, On the endomorphisms of \?\?\?(\?\textonesuperior _{\?}(\?)) when \?=1 and \? has general moduli, Classification of irregular varieties (Trento, 1990) Lecture Notes in Math., vol. 1515, Springer, Berlin, 1992, pp. 41 -- 67.

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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) flag varieties; Kac-Moody group; generalized Cartan matrix; Kac-Moody Lie algebra; Lie algebra cohomology; formal DG-algebra; \(\mathbb Q\)-formal space; rational homotopy theory; minimal model; homotopy Lie algebra Kumar, S.: Rational homotopy theory of flag varieties associated to Kac-Moody groups. MSRI publications 4, 233-273 (1985)

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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) proof of Mordell conjecture; proof of Tate conjecture; proof of; Shafarevich conjecture; height of Abelian variety; rational points; on elliptic curves Deligne, P., Preuve des conjectures de Tate et de shafarevitch (d'après G. faltings), Asterisque, 121-122, 25-41, (1985)

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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) stable sheaf on variety of dimension bigger than one; complete intersection curve; stable bundle with zero Chern classes; irreducible unitary representation of fundamental group V.B. Mehta and A. Ramanathan, Restriction of stable sheaves and representations of the fundamental group. Inv. Math. 77 (1984), pp. 163--172.

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) extensions of function field; generic Galois extension; Kummer theory; Leopoldt's conjecture; cyclotomic fields; geometric class field theory C. Greither, Cyclic Galois extensions of commutative rings. Lecture Notes in Mathematics, vol. 1534. Springer, Berlin-Heidelberg-New York, 1992. Zbl0788.13003 MR1222646