Heegner modules and elliptic curves
Heegner points on both modular curves and elliptic curves over global fields of any characteristic is 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 being equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields. TOC:Preface.- 1. Introduction.- 2. Preliminaries.- 3. Bruhat-Tits trees with complex multiplication.- 4. Heegner sheaves.- 5. The Heegner module.- 6. Cohomology of the Heegner module.- 7. Finiteness of the Tate-Shafarevich groups.- Appendix A. Rigid analytic modular forms.- Appendix B. Automorphic forms and elliptic curves over function fields.- References.- Index.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
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9783540222903
3540222901
- Dimensions
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24 cm
- Extent
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X, 517 S.
- Language
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Englisch
- Notes
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Literaturverz. S. 507 - 510
- Bibliographic citation
-
Lecture notes in mathematics ; 1849
- Classification
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Mathematik
- Keyword
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Elliptische Kurve
Heegner-Punkt
Drinfeld-Modul
- Event
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Veröffentlichung
- (where)
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Berlin, Heidelberg, New York
- (who)
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Springer
- (when)
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2004
- Creator
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Brown, Martin L.
- Table of contents
- Rights
-
Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Last update
-
11.03.2025, 12:25 PM CET
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Brown, Martin L.
- Springer
Time of origin
- 2004
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