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Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

 
 
 
 
Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)
Author: Joseph H. Silverman
ISBN 13: 9780387943282
ISBN 10: 387943285
Edition: N/A
Publisher: Springer
Publication Date: 1999-09-24
Format: Paperback
Pages: 528
List Price: $59.95
 
 

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.