Advanced Topics in the Arithmetic of Elliptic Curves / Edition 1

Advanced Topics in the Arithmetic of Elliptic Curves / Edition 1

by Joseph H. Silverman
     
 

ISBN-10: 0387943285

ISBN-13: 9780387943282

Pub. Date: 11/04/1994

Publisher: Springer New York

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

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Overview

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.

Product Details

ISBN-13:
9780387943282
Publisher:
Springer New York
Publication date:
11/04/1994
Series:
Graduate Texts in Mathematics Series, #151
Edition description:
Softcover reprint of the original 1st ed. 1994
Pages:
528
Sales rank:
942,639
Product dimensions:
1.11(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface
Computer Packages
Acknowledgments
Introduction1
Ch. IElliptic and Modular Functions5
Ch. IIComplex Multiplication95
Ch. IIIElliptic Surfaces187
Ch. IVThe Neron Model289
Ch. VElliptic Curves over Complete Fields408
Ch. VILocal Height Functions454
App. A: Some Useful Tables481
Notes on Exercises484
References488
List of Notation498
Index504

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