1.

Record Nr.

UNISA996466476203316

Autore

Brown Martin L

Titolo

Heegner Modules and Elliptic Curves [[electronic resource] /] / by Martin L. Brown

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004

ISBN

3-540-44475-0

Edizione

[1st ed. 2004.]

Descrizione fisica

1 online resource (X, 518 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1849

Disciplina

512.3

Soggetti

Number theory

Algebraic geometry

Number Theory

Algebraic Geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

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.

Sommario/riassunto

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.