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Heegner Modules and Elliptic Curves de Martin L. Brown

Heegner Modules and Elliptic Curves: Lecture Notes in Mathematics, cartea 1849

Autor Martin L. Brown
en Limba Engleză Paperback – 15 iul 2004
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.
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Specificații

ISBN-13: 9783540222903
ISBN-10: 3540222901
Pagini: 532
Ilustrații: X, 518 p.
Dimensiuni: 155 x 235 x 29 mm
Greutate: 0.8 kg
Ediția:2004
Editura: SPRINGER VIEWEG
Colecția Lecture Notes in Mathematics
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Textul de pe ultima copertă

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.