Heegner Modules and Elliptic Curves [[electronic resource] /] / by Martin L. Brown
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| Autore: |
Brown Martin L
|
| Titolo: |
Heegner Modules and Elliptic Curves [[electronic resource] /] / by Martin L. Brown
|
| Pubblicazione: | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 |
| Edizione: | 1st ed. 2004. |
| Descrizione fisica: | 1 online resource (X, 518 p.) |
| Disciplina: | 512.3 |
| Soggetto topico: | Number theory |
| Algebraic geometry | |
| Number Theory | |
| Algebraic Geometry | |
| 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. |
| Titolo autorizzato: | Heegner modules and elliptic curves |
| ISBN: | 3-540-44475-0 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 996466476203316 |
| Lo trovi qui: | Univ. di Salerno |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes in Mathematics, . 0075-8434 ; ; 1849