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EnglishLet E/F be a modular elliptic curve defined over a totally real number field F and let f be its associated eigenform. This article presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of E over suitable quadratic imaginary extensions K/F. In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachev, that is, when [F : Q] is even and phi not new at any prime.
| Titolo: | On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields |
| Autori: | |
| Data di pubblicazione: | 2006 |
| Rivista: | |
| Abstract: | Let E/F be a modular elliptic curve defined over a totally real number field F and let f be its associated eigenform. This article presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of E over suitable quadratic imaginary extensions K/F. In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachev, that is, when [F : Q] is even and phi not new at any prime. |
| Handle: | http://hdl.handle.net/11577/152514 |
| Appare nelle tipologie: | 01.01 - Articolo in rivista |
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