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Heegner Modules and Elliptic Curves

  • Book
  • © 2004

Overview

Authors:
  1. Martin L. Brown
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1849)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
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  2. 1. Introduction

    • Martin L. Brown
    Pages 1-11

  3. 2. Preliminaries

    • Martin L. Brown
    Pages 13-30

  4. 3. Bruhat-Tits trees with complex multiplication

    • Martin L. Brown
    Pages 31-74

  5. 4. Heegner sheaves

    • Martin L. Brown
    Pages 75-103

  6. 5. The Heegner module

    • Martin L. Brown
    Pages 105-222

  7. 6. Cohomology of the Heegner module

    • Martin L. Brown
    Pages 223-327

  8. 7. Finiteness of Tate-Shafarevich groups

    • Martin L. Brown
    Pages 329-434

  9. Appendix

    • Martin L. Brown
    Pages 435-505

  10. References

    • Martin L. Brown
    Pages 507-510

  11. Index

    • Martin L. Brown
    Pages 511-517

  12. Back Matter

    Pages 519-519
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Heegner Modules and Elliptic Curves

  • Authors: Martin L. Brown

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b98488

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2004

  • Softcover ISBN: 978-3-540-22290-3Published: 15 July 2004

  • eBook ISBN: 978-3-540-44475-6Published: 30 August 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 518

  • Topics: Number Theory, Algebraic Geometry

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