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HEEGNER MODULES AND ELLIPTIC CURVES 🔍
Brown, M. L. (martin L.), Martin L. Brown, M. L Brown Springer Berlin Heidelberg : Imprint : Springer, 2004, 2004
英语 [en] · PDF · 99.4MB · 2004 · 📗 未知类型的图书 · 🚀/duxiu/zlibzh · Save
描述
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. Preface -- Introduction -- Preliminaries -- Bruhat-tits Trees With Complex Multiplication -- Heegner Sheaves -- The Heegner Module -- Cohomology Of The Heegner Module -- Finiteness Of The Tate-shafarevich Groups -- Appendix A.: Rigid Analytic Modular Forms -- Appendix B.: Automorphic Forms And Elliptic Curves Over Function Fields -- References -- Index. M.l. Brown. Includes Bibliographical References (p. [507]-510) And Index.
备用文件名
zlibzh/no-category/Brown, M. L. (martin L.), Martin L. Brown, M. L Brown/a_29961932.pdf
备用出版商
Springer Spektrum. in Springer-Verlag GmbH
备用出版商
Steinkopff. in Springer-Verlag GmbH
备用出版商
Springer London, Limited
备用出版商
Springer Nature
备用版本
Lecture notes in mathematics (Springer-Verlag), 1849, Berlin ; New York, ©2004
备用版本
Lecture Notes in Mathematics, Berlin, Heidelberg, 2004
备用版本
Lecture notes in mathematics <Berlin>, Berlin, 2004
备用版本
1 edition, August 26, 2004
备用版本
Germany, Germany
备用版本
1, 20040830
备用版本
2004, 2007
元数据中的注释
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filepath:/读秀/读秀4.0/读秀/4.0/数据库41-1/a_40355583.zip
元数据中的注释
Lecture Notes in Mathematics
备用描述
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
备用描述
The points of departure of this text are twofold: first the proof by Drinfeld in 1974 ([Drl], see also Appendix B) of an important case of the Langlands conjecture for GL2 over a global field of positive characteristic and second the proof by Kolyvagin [K] in 1989 of the Birch Swinnerton-Dyer conjecture for a class of Weil elliptic curves over the rational field Q.
备用描述
Lecture Notes in Mathematics
Erscheinungsdatum: 15.07.2004
开源日期
2024-06-13
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