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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) curve; function field; Jacobian; abelian variety; finite field; Mordell-Weil group; torsion; rank; \(L\)-function; Birch and Swinnerton-Dyer conjecture; Tate-Shafarevich group; Tamagawa number; endomorphism algebra; descent; height; Néron model; Kodaira-Spencer map; monodromy

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 function field; rational division points; twist; Mordell-Weil group Wang, W. B., On the twist of abelian varieties defined by the Galois extension of prime degree, J. Algebra, 163, 3, 813-818, (1994)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; Jacobian; Mordell-Weil group; function field; rank Ulmer, D., On Mordell-Weil groups of Jacobians over function fields, J. Inst. Math. Jussieu, 12, 1, 1-29, (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) integral points on algebraic curves; rational point; Jacobian; linear form of logarithms; Mordell-Weil group; height Hirata-Kohno N. , Une relation entre les points entiers sur une courbe algébrique et les points rationnels de la jacobienne , in: Advances in Number Theory , Kingston, ON, 1991 , Oxford University Press , New York , 1993 , pp. 421 - 433 . MR 1368438 | Zbl 0805.14009

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 a finite field; rational point; Weil bound; 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) Mordell-Weil rank; abelian variety; function field; Prym variety; Jacobian variety

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil group; Picard variety; Function field; Tate conjecture; L-function; Birch--Swinnerton-Dyer conjecture Hindry M., Pacheco A., Wazir R.: Fibrations et conjecture de Tate. J. Number Theory 112, 345--368 (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) abelian variety; function field; finitely generated field; Selmer group; Shafarevich-Tate group; discrete Selmer group; discrete Shafarevich-Tate group; 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) Mordell-Weil group; Picard variety; function field; Tate conjecture; L-function Hindry, M., Pacheco, A.: Sur le rang des Jacobiennes sur un corps de fonctions. Bull. Soc. Math. Fr. 133, 275--295 (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) abelian variety; Jacobian variety; Selmer group; Mordell-Weil group; Iwasawa 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) Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 1996.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 the rational function field; ring of invariants; excellent families of elliptic curves; Weyl group; Mordell-Weil lattice of a rational elliptic surface Shioda, T; Usui, H, Fundamental invariants of Weyl groups and excellent families of elliptic curves, Comment. Math. Univ. St. Pauli, 41, 169-217, (1992)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 groups; genus 2 curves; Jacobian variety; Kummer surfaces; torsion group; rational points; computer algebra; Diophantine equations Cassels, J. W. S.; Flynn, E. V., Prolegomena to a Middlebrow Arithmetic of Curves of Genus \(2\), London Mathematical Society Lecture Note Series 230, xiv+219 pp., (1996), Cambridge University 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) Mordell-Weil lattice; elliptic curve over function field of rank 8; rational points generating 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) rational points; Jacobian variety; Mordell-Weil group; Mordell-Weil lattice Saitō, M-H; Sakakibara, K-I, On Mordell-Weil lattices of higher genus fibrations on rational surfaces, J. Math. Kyoto Univ., 34, 859-871, (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) field of definition of the Mordell-Weil group; elliptic curve; Mordell- Weil theorem; rational points; jacobian; Galois action Masato Kuwata, The field of definition of the Mordell-Weil group of an elliptic curve over a function field, Compositio Math. 76 (1990), no. 3, 399 -- 406.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 function field; Mordell-Weil group; rational points; elliptic surface; Kodaira-Néron model; Néron-Severi group; Mordell- Weil lattice; height pairing F. Denef, \textit{Les Houches lectures on constructing string vacua}, arXiv:0803.1194 [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) rational function field; automorphism group; Ree group; Hasse-Weil bound Pedersen, J.P.: A function field related to the Ree group. In: Coding Theory and Algebraic Geometry, Lecture Notes in Mathematics, vol. 1518, pp. 122--132. Springer, Berlin (1992)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 conjecture; Rational points; Seminar; Bonn/Germany; Wuppertal/Germany; proof of Tate conjecture; proof of Shafarevich conjecture; proof of the Mordell conjecture; logarithmic singularities; compactification of the moduli space of abelian varieties; modular height of an abelian variety; p-divisible groups; intersection theory on arithmetic surfaces; Riemann- Roch theorem; Hodge index theorem; rational points G. FALTINGS - G. WÜSTHOLZ, Rational points, Aspects of Math., Vieweg, 1986. Zbl0636.14019 MR863887

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 of genus 2; Mordell-Weil group; Mordell-Weil rank; rational points; absolutely simple Jacobian; high rank

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) invariants of finite group; inverse problem of Galois theory; Noether's problem; function field of a torus; Algebraic Tori; rational points of tori Swan, R. G.: Noether's problems in Galois theory. Symposium ''emmy Noether in bryn mawr'' (1983)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; abelian variety; Iwasawa algebra; universal norms of a commutative formal group; rational points of a toroidal formal group; \({\mathbb{Z}}_ p\)-extension; complex multiplication Wingberg, K, On the rational points of abelian varieties over \({\mathbb{Z}}_{p}\)-extensions of number fields, Math. Ann., 279, 9-24, (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) Model theory; Algebraic geometry; Mordell-Lang conjecture; abelian variety; model-theoretic stability; omega-stable group; Zariski geometry; differentially closed field; separably closed field Bouscaren E. (eds) (1998) Model Theory and Algebraic Geometry: An Introduction to E. Hrushovski's Proof of the Geometric Mordell-Lang Conjecture. Springer-Verlag, New York

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 of a hyperelliptic curve; group of rational points; finite field; Weil pairing

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; elliptic curve; function field; elliptic \(K3\)-surface; rank Chahal, Jasbir and Meijer, Matthijs and Top, Jaap, Sections on certain {\(j=0\)} elliptic surfaces, Commentarii Mathematici Universitatis Sancti Pauli, 49, 1, 79-89, (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) Mordell-Weil group; Néron-Severi group of an elliptic surface; intersection theory; Mordell-Weil lattice of an elliptic surface; height pairing Tetsuji Shioda, ``On the Mordell-Weil lattices'', Comment. Math. Univ. St. Pauli39 (1990) no. 2, p. 211-240

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) cohomological Hasse principle; zeta function; Chow group; Bloch map; unramified class field theory, étale cohomology, cycle map, Milnor \(K\)-group; intersection theory; arithmetic geometry; algebraic cycle

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 measure; rational points; abelian variety; rank; Mordell-Weil group; Néron-Tate height Waldschmidt M.: Density measure of rational points on abelian varieties. Nagoya Math. J. 155, 27--53 (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) Mordell-Weil groups of elliptic curves with complex; multiplication; Weil parametrizations; L-function attached to a Weil curve; anti-cyclotomic tower; Iwasawa theory of elliptic curves; p-adic height pairing; p-adic L-functions; p-adic Heegner measures; finiteness of the Tate-Shafarevich group; Mordell-Weil groups of elliptic curves with complex multiplication B. Mazur, Modular curves and arithmetic, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 185 -- 211.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; higher \(K\)-group; elliptic curve; Mordell-Weil group; Dwyer-Friedlander maps; Kummer theory G. Banaszak, W. Gajda, P. Krasoń, Detecting linear dependence by reduction maps, Jour. of Number Theory 115 (2005), no. 2, 322--342.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rationality questions; rational points; Hasse-Weil \(L\)-function of modular elliptic curves; local-global principles; Selmer's curve; smooth projective varieties; Tate-Shafarevich group; Tate-Shafarevich conjecture; Selmer groups of elliptic curves; class field theory; Kolyvagin test classes Mazur B.: On the passage from local to global in number theory. Bull. Amer. Math. Soc. (N.S.) 29(1), 14--50 (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) curve; function field; finite field; genus; rational point; Hasse-Weil bound Anbar, N; Stichtenoth, H, Curves of every genus with a prescribed number of rational points, Bull. Braz. Math. Soc. (N.S.), 44, 173-193, (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) Galois theory; Galois group; full automorphism group; Galois extension; inverse Galois problem; separably generated extension; solvable group; algebraic function field; rational function field; ramified; perfect field; genus; place; Castelnuovo-Severi inequality

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rank of group of rational points; Jacobian; Mordell-Weil rank; hyperelliptic curve Schaefer, Edward F., \(2\)-descent on the Jacobians of hyperelliptic curves, J. Number Theory, 51, 2, 219-232, (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) Jacobian variety; rational points; linear pencil of projective plane curves; Mordell-Weil lattices; Manin-Shafarevich theorem; height pairing; Lefschetz pencils of hyperplane sections Shioda, T.: Generalization of a theorem of Manin-Shafarevich. Proc. Japan acad. 69A, 10-12 (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) Tate module; arithmetic fundamental group; Galois representation; Fontaine-Mazur conjecture; cyclic covering; rational point; Galois group of function field; large quotient; moduli space of abelian varieties G. Frey and E. Kani, Projective p-adic representations of the k-rational geometric fundamental group, Archiv der Mathematik 77 (2001), 32--46.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 conjecture; number of rational points; Vojta's method; Faltings theorem; genus; rank of Mordell-Weil group; Jacobian; points of small height; modular 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) wave turbulence theory; \(\beta\)-plane; Rossby wave; drift wave; Charney-Hasegawa-Mima equation; conservation of potential vorticity; resonance; arithmetic geometry; Diophantine equation; elliptic curve; rational elliptic surface; Mordell-Weil group; Chabauty-Coleman method

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) capacity theory; arithmetic intersection theory; projective variety over a number field; Green's function Chinburg, T., Lau, C. F., and Rumely, R. Capacity theory and arithmetic intersection theory,Duke Math. J. 117(2), 229--285, (2003).

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic variety; bivariant theory; intersection product; Chern-Schwartz-MacPherson class; specialization; Grothendieck transformation; characteristic function; Chow group; push-forward; pull-back L Ernström, S Yokura, Bivariant Chern-Schwartz-MacPherson classes with values in Chow groups, Selecta Math. 8 (2002) 1

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 cohomology; geometry of a generic point; Galois group of the algebraic closure of the field of rational functions on the variety; étale cohomology Bogomolov F.A., Stable cohomology of groups and algebraic varieties, Russian Acad. Sci. Sb. Math., 1993, 76(1), 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) rational map; rank of Mordell-Weil group; rational points; family of elliptic curves; cyclic cubic 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) abelian variety; Jacobian variety; Mordell-Weil rank; cyclic cover of the projective line; infinite field extension; idempotent relation DOI: 10.1006/jnth.2001.2692

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; 11-torsion; 2-descent; elliptic curve; rational point of order 11; Birch Swinnerton-Dyer conjecture Ian Connell, Elliptic curve handbook, preprint, available at http://www.ucm.es/ BUCM/mat/doc8354.pdf.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) adelic modular group; modular curve; no rational points over any quadratic field; torsion groups; elliptic curve; Mordell-Weil groups Najman, F.: Torsion of rational elliptic curves over cubic fields and sporadic points on \(X_1(n)\). arXiv: 1211.2188.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) semiabelian variety; Mordell-Lang conjecture; finite field; integral point; Frobenius map; F-structure; stable theory; quantifier elimination Moosa, Rahim; Scanlon, Thomas, \(F\)-structures and integral points on semiabelian varieties over finite fields, Amer. J. Math., 126, 3, 473-522, (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) elliptic curves over the rational field; Diophantine \(m\)-tuple; high rank; rational points; Mordell-Weil group A. Dujella, Irregular Diophantine \(m\)-tuples and elliptic curves of high rank, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 5, 66-67.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; purely inseparable; strongly semistable; rational point; function field; Harder-Narashima filtration Rössler, D.: On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic, Comment. math. Helv. 90, No. 1, 23-32 (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) textbook; partially ordered sets; Zorn's lemma; number theory; fields; rings; abelian groups; polynomials; field extension; formal power series; polynomial rings; finite fields; power series; rational function; Bernoulli numbers; Puiseux series; Laurent series; ideals; quotient rings; factorization; Noetherian rings; prime ideals; principal ideal domains; cyclic groups; homomorphism; group action; quotient group; symmetric group; semidirect product; Sylow group; modules; free modules; commutative ring; Smith normal form; elementary divisor; Jordan form; Hermitian space; projective space; bilinear form; symplectic space; quadratic form; Kähler triples; quaternions; spinors

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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-Manin obstruction; Mordell-Lang conjecture; abelian varieties; function field; rational point Bjorn Poonen and José Felipe Voloch, The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields, Ann. of Math. (2) 171 (2010), no. 1, 511 -- 532.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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-Lang conjecture; rational points; torsion points; algebraically closed field; semi-Abelian variety; differentially closed field; group subvarieties; separably closed fields; Hrushovski-Zil'ber Dichotomy Theorem; diophantine geometry; Zariski geometry Manin, Y.I.: Letter to the editors: ''Rational points on algebraic curves over function fields'' [Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 1397-1442; MR0157971 (28 #1199)], Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 2, 447-448 (Russian); English transl., Math. USSR-Izv. 34 (1990), no. 2, 465-466

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; quartic curve; Weierstrass points; Mordell-Weil group; isogeny; CM elliptic curve Matthew J. Klassen and Edward F. Schaefer, Arithmetic and geometry of the curve \?³+1=\?\(^{4}\), Acta Arith. 74 (1996), no. 3, 241 -- 257.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) isomorphism classes of elliptic curves; rational point of order p; finite Mordell-Weil group Kamienny, S, Torsion points on elliptic curves over all quadratic fields. duke, Math. J, 53, 157-162, (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) boundedness conjecture for group of rational torsion points; elliptic curve; Mordell-Weil theorem; abelian variety; potential complex multiplication; torsion points on the Fermat curves; p-adic abelian integrals Coleman, Robert F., Torsion points on curves and \textit{p}-adic abelian integrals, Ann. of Math. (2), 121, 1, 111-168, (1985), MR782557

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 representations; Mordell-Weil lattices; elliptic curves; deformation theory of isolated singularities; Mordell-Weil group; Hasse zeta function; elliptic surfaces; Artin L-function; Weil height; del Pezzo surfaces; cubic forms Shioda, T.: Mordell-Weil lattices and Galois representation. I, II, III. Proc. Japan Acad., 65A, 269-271 ; 296-299 ; 300-303 (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) finiteness of Tate-Shafarevich group; abelian varieties with real multiplication; higher-dimensional elliptic curve; Jacobian of a Shimura curve; Heegner point; Mordell-Weil group Ярощук, В. А., Интегральный инвариант в задаче о качении эллипсоида со специальными распределениями масс по неподвижной поверхности без проскальзывания, Изв. РАН. Мех. тв. тела, 2, 54-57, (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) Elliptic curves; Mordell-Weil rank; Lang's conjecture; rational point; variety of general type

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

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 theorem; rational points; \(p\)-descent; Selmer group; \(L\)- function; conjecture of Birch and Swinnerton-Dyer; Igusa curves Ulmer, D. L., P-descent in characteristic p, Duke Math. J., 62, 2, 237-265, (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 points of an elliptic curve; Mordell-Weil group; L-function; Tate-Shafarevich group; conjecture of Taniyama and Weil; Fermat problem Zagier, D.: Elliptische Kurven: Fortschritte und Anwendungen. Jahresberichte der Deutschen Mathematiker-Vereinigung 92, 58--76 (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) rationality of moduli space; rank two quiver; rational matrix invariants; stable vector bundles over the projective plane; function field of the generic Jacobian variety Le Bruyn, L., Some remarks on rational matrix invariants.J. Algebra, 118 (1988), 487--493.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; hyperelliptic curves; Weierstrass point; Mordell-Weil group M. Bhargava, B.H. Gross, The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point, in \(Automorphic Representations and L-Functions\). Tata Institute of Fundamental Research Studies in Mathematics, vol. 22 (Tata Institute of Fundamental Research, Mumbai, 2013), pp. 23-91

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; Seminar; Bonn; Wuppertal; Mordell conjecture; proof of Tate conjecture; proof of Shafarevich conjecture; proof of the Mordell conjecture; logarithmic singularities; compactification of the moduli space of abelian varieties; modular height of an abelian variety; p-divisible groups; intersection theory on arithmetic surfaces; Riemann-Roch theorem; Hodge index theorem G. Faltings , G. Wüstholz , Rational Points, Aspects of Mathematics No. E6 , Vieweg, Braunschweig/Wiesbaden, 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) proof of the conjecture of Birch and Swinnerton-Dyer for an abelian variety over a function field; Hasse-Weil zeta-function; Tate-Shafarevich group; prime characteristic

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) arithmetic of elliptic curves; determining the group of rational points; Mordell-Weil theorem; Birch and Swinnerton-Dyer conjecture; Hasse-Weil L-series; effective determination of all imaginary quadratic fields with given class number; Iwasawa theory; main conjecture for elliptic curves; descent method Coates, J.: Elliptic curves and Iwasawa theory. In: Modular forms. Rankin, R.A. (ed.), pp. 51-73. Chichester: Ellis Horwood Ltd (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) curves over finite field; rational point; Weil bound; Toeplitz matrices; zeta 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) Galois cohomology; descent; Selmer group; theorem of Mordell-Weil; abelian variety; Iwasawa module; Tate-Shafarevich-group; p-adic zeta function; p-adic analytic group Harris, M, \(p\)-adic representations arising from descent on abelian varieties, Compos. Math., 39, 177-245, (1979)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 of the modular curve; modular elliptic curve; class number problem; infinite order point in Mordell-Weil group; heights of Heegner points; Rankin L-series; holomorphic continuations; functional equations; conjecture of Birch and Swinnerton-Dyer Gross, B. H.; Zagier, D. B., Heegner points and derivatives of \textit{L}-series, Invent. Math., 84, 225-320, (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) pseudo real closed field; absolute Galois group; prc-field; orderings; variety; rational point; absolute Galois e-structure; profinite group; projectivity Basarab, S. A., The absolute Galois group of a pseudo real closed field with finitely many orders, J. Pure Appl. Algebra, 38, 1-18, (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) Jacobian variety; superelliptic curves; 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) hyperelliptic curve; function field; finite field; Jacobian variety; class group; two-torsion [5]G. Cornelissen, Two-torsion in the Jacobian of hyperelliptic curves over finite fields, Arch. Math. (Basel) 77 (2001), 241--246.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 Lie algebras; abelian varieties; modular invariant; partition function; rational conformal field theory; Jacobian of a Fermat curve; triangulated surfaces; Riemann surface M. Bauer, A. Coste, C. Itzykson and P. Ruelle, ''Comments on the links between SU(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards,'' J. Geom. Phys. 22 (1997), 134--189.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) automorphic representation; Deligne conjecture; Langlands correspondence; Poincaré function; Hecke algebra; cuspidal spectrum; trace formula; characteristic morphism; Drinfeld modular variety; \(\ell\)-adic cohomology; intersection cohomology; Satake compactification; rationality results; Grothendieck group of admissible representations; reduction theory; orbital integrals Laumon, Gérard, Cohomology of Drinfeld modular varieties. Part II, Cambridge Studies in Advanced Mathematics 56, xii+366 pp., (1997), Cambridge University 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) rational point; ring of integers of a number field; Arakelov class group; hermitian line bundle; arithmetic variety Agboola A. and Pappas G. (2000). Lines bundles, rational points and ideal classes. Math. Res. Lett. 7: 1--9

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 Weierstrass points; Jacobian; 2-descent; Tate-Shafarevich group; Mordell-Weil rank D. Gordon and D. Grant, Computing the Mordell-Weil rank of Jacobians of curves of genus two , Trans. Amer. Math. Soc. 337 (1993), no. 2, 807-824. JSTOR:

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 of rational function field over complex 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) difference field; abelian variety; theory ACFA; group definable in a model; model theoretic stability; 1-basedness; Manin-Mumford conjecture; model companion of the theory of fields with an automorphism Z. Chatzidakis, ''Groups definable in ACFA,'' in Algebraic Model Theory, Dordrecht: Kluwer Acad. Publ., 1997, vol. 496, pp. 25-52.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 non-rational subfields; number of separable subfields; number of morphisms of algebraic curves; Chow coordinates; theorem of the base; Jacobian; genus; function field; Angle theorem; de Franchis' theorem E. Kani, Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. Zbl0615.12017 MR842053

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 lattice structure of the Mordell-Weil group; height pairing; L-function; Hasse zeta function; computer calculations Shioda, T.: The Galois Representations of TypeE 8 Arising from Certain Mordell-Weil Groups, Proc. Japan Acad.65A, 195--197 (1989)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) modular curve; jacobian; abelian variety; \({\mathbb{Q}}\)-simple factors; torsion subgroups of the Mordell-Weil groups; conjecture of Birch and Swinnerton-Dyer

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) conjecture of Beilinson and Bloch; rank of the Griffiths group; smooth projective variety over a number field; order of vanishing of an L-function; elliptic curves J. Buhler, C. Schoen, and J. Top, ''Cycles, \(L\)-functions and triple products of elliptic curves,'' J. reine angew. Math., vol. 492, pp. 93-133, 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) Jacobian fibration; elliptic fibration; Mordell-Weil group; height pairing; K3 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) Weil conjectures; finite ground field; number of rational points; coding theory Sørensen, A. B., On the number of rational points on codimension-1 algebraic sets in \(\mathbb{P}^n(\mathbb{F}_q)\), Discrete Math., 135, 321-334, (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) 2-dimensional Cremona group; algebraic automorphism; automorphism of the rational function field; birational automorphisms D. Wright, Two-dimensional Cremona groups acting on simplicial complexes, Trans. Amer. Math. Soc. 331 (1992), no. 1, 281--300.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 numbers; rank of the Mordell-Weil group; elliptic curves over function fields; automorphisms Peter F. Stiller, The Picard numbers of elliptic surfaces with many symmetries, Pacific J. Math. 128 (1987), no. 1, 157 -- 189.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 cycles; Weil conjectures; zeta-function; algebraic variety; finite field Kleiman, S.: Algebraic cycles and the Weil conjectures. In: Grothendieck, A. et al. (eds.) Dix Exposés sur la Cohomologie des Schémas, pp. 359-386. North-Holland, Amsterdam (1968)

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) cross ratio variety; rational double point; Weyl groups; Appell- Lauricella hypergeometric function; deformation of \(E_ 6\)-singularity; cubic surface; Cayley family J. Sekiguchi: The versal deformation of the \(E_6\)-singularity and a family of cubic surfaces , J. Math. Soc. Japan 46 (1994), 355--383.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Mordell-Weil group; rank; 7-torsion points; rational points O. Lecacheux, Rang de familles de courbes elliptiques. Acta Arith. 109(2) (2003), 131-142. Zbl1036.11022 MR1980641

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

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

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Calabi-Yau 3-folds; Mordell-Weil rank; rational elliptic surfaces; elliptic fibration; Schoen 3-folds; Namikawa examples; quantum gravity; abelian gauge algebra; F-theory compactification; massless particle spectrum; U(1) charge; charged singlet matter; anomaly cancellation; Weierstrass model; Elkies models; birational Calabi-Yau

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 module; abelian variety; function field; Galois group; transcendence degree О группах галуа функциональных полей над полями конечного типа над, УМН, 46, 5-281, 163-164, (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) transcendence theory; linear dependence; algebraic points; algebraic group; generators; logarithmic heights; dependence relations; abelian variety; Neron-Tate height; Weil's height Masser ( D.W. ) .- Linear relations on algebraic groups , in New Advances in Transcendence Theory (ed. A. Baker), Cambridge Univ. Press , chap. 15 ( 1988 ), pp. 248 - 262 . MR 972004 | Zbl 0656.10031

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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; Mordell-Weil lattices; 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) varieties over a local field; Néron models; arithmetical graphs; discrete valuation ring; Jacobian; abelian variety; group of components Lorenzini, D., Reduction of points in the group of components of the Néron model of a Jacobian, J. Reine Angew. Math., 527, 117-150, (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) number of points of Jacobians; finite field; class number; Weil-Riemann hypothesis; rational point [LMD]G. Lachaud and M. Martin-Deschamps, Nombre de points des jacobiennes sur un corps fini, Acta Arith. 56 (1990), 329--340.

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 of subfields; stable points; automorphism action; moduli space; rational function field; affine algebraic variety; Bezout form

rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New 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 point; counting multiplicities; height function over projective space; intersection tree; rational point