Overview

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.

Full Product Details

Author:   Martin L. Brown
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2004 ed.
Volume:   1849
Dimensions:   Width: 15.50cm , Height: 2.70cm , Length: 23.50cm
Weight:   1.630kg
ISBN:  

9783540222903

ISBN 10:   3540222901
Pages:   518
Publication Date:   15 July 2004
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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