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- About this book
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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.
- Table of contents (10 chapters)
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1. Introduction
Pages 1-11
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2. Preliminaries
Pages 13-30
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3. Bruhat-Tits trees with complex multiplication
Pages 31-74
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4. Heegner sheaves
Pages 75-103
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5. The Heegner module
Pages 105-222
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Heegner Modules and Elliptic Curves
- Authors
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- Martin L. Brown
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 1849
- Copyright
- 2004
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-44475-6
- DOI
- 10.1007/b98488
- Softcover ISBN
- 978-3-540-22290-3
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- X, 518
- Topics