The theme of this work is the study of the Nekovar{Selmer group attached to a twisted Hida family T of Galois representations and a quadratic number eld K. The results that we obtain have the following shape: if a twisted L-function of a suitable modular form in the Hida family has order of vanishing r 1 at the central critical point then the rank of the Selmer group of the Hida family over K as a module over a certain local Hida-Hecke algebra is equal to r.
Vanishing of special values and central derivatives in Hida families
LONGO, MATTEO;
2014
Abstract
The theme of this work is the study of the Nekovar{Selmer group attached to a twisted Hida family T of Galois representations and a quadratic number eld K. The results that we obtain have the following shape: if a twisted L-function of a suitable modular form in the Hida family has order of vanishing r 1 at the central critical point then the rank of the Selmer group of the Hida family over K as a module over a certain local Hida-Hecke algebra is equal to r.File in questo prodotto:
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