Advanced topics in the arithmetic of elliptic curves / Joseph H. Silverman

Auteur: Silverman, Joseph H. (1955-) - AuteurType de document: MonographieCollection: Graduate texts in mathematics ; 151Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, cop. 1994Description: 1 vol. (XIII-525 p.) : fig. ; 25 cm ISBN: 0387943250 ; rel. Résumé: In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Néron models, Kodaira-N ron classification of special fibres, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Néron's theory of canonical local height functions. (Source : Springer).Bibliographie: Bibliogr. p. 488-497. Index. Sujets MSC: 14H52 Algebraic geometry -- Curves -- Elliptic curves
14G40 Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights
11-02 Number theory -- Research exposition (monographs, survey articles)
11Gxx Number theory -- Arithmetic algebraic geometry (Diophantine geometry)
14-02 Algebraic geometry -- Research exposition (monographs, survey articles)
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Bibliogr. p. 488-497. Index

In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Néron models, Kodaira-N ron classification of special fibres, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Néron's theory of canonical local height functions. (Source : Springer)

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