Heegner Modules and Elliptic Curves

  • Authors
  • Martin L. Brown

Part of the Lecture Notes in Mathematics book series (LNM, volume 1849)

Table of contents

  1. Front Matter
    Pages I-X
  2. Martin L. Brown
    Pages 1-11
  3. Martin L. Brown
    Pages 13-30
  4. Martin L. Brown
    Pages 75-103
  5. Martin L. Brown
    Pages 105-222
  6. Martin L. Brown
    Pages 223-327
  7. Martin L. Brown
    Pages 329-434
  8. Martin L. Brown
    Pages 435-505
  9. Martin L. Brown
    Pages 507-510
  10. Martin L. Brown
    Pages 511-517
  11. Back Matter
    Pages 519-519

About this book

Introduction

Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields; this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.

Keywords

Drinfeld Modules Elliptic Curves Heegner Points Tate Conjecture Tate-Shafarevich Groups finite field

Bibliographic information

  • DOI https://doi.org/10.1007/b98488
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-22290-3
  • Online ISBN 978-3-540-44475-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book