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Advanced Topics in the Arithmetic of Elliptic Curves / Edition 1

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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.

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Product Details

  • ISBN-13: 9780387943282
  • Publisher: Springer New York
  • Publication date: 11/4/1994
  • Series: Graduate Texts in Mathematics Series , #151
  • Edition description: Softcover reprint of the original 1st ed. 1994
  • Edition number: 1
  • Pages: 528
  • Product dimensions: 1.11 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface
Computer Packages
Acknowledgments
Introduction 1
Ch. I Elliptic and Modular Functions 5
Ch. II Complex Multiplication 95
Ch. III Elliptic Surfaces 187
Ch. IV The Neron Model 289
Ch. V Elliptic Curves over Complete Fields 408
Ch. VI Local Height Functions 454
App. A: Some Useful Tables 481
Notes on Exercises 484
References 488
List of Notation 498
Index 504
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