Euler systems obtained from congruences between Hilbert modular forms
On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields
Let be a modular elliptic curve defined over a totally real number field and let be its associated eigenform. This paper presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of over suitable quadratic imaginary extensions . In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachëv, that is, when is even and not new at any prime.
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