Heegner Modules and Elliptic Curves

2004
ISBN: 978-3-540-22290-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1849, 518 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1630 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Brown, Martin L.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.