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### Fine Selmer group of Hida deformations over non-commutative $p$-adic Lie extensions

Somnath Jha
Source: Asian J. Math. Volume 16, Number 2 (2012), 353-366.

#### Abstract

We study the Selmer group and the fine Selmer group of $p$-adic Galois representations defined over a non-commutative $p$-adic Lie extension and their Hida deformations. For the fine Selmer group, we generalize the pseudonullity conjecture of J. Coates and R. Sujatha, "Fine Selmer group of elliptic curves over $p$-adic Lie extensions," in this context and discuss its invariance in a branch of a Hida family. We relate the structure of the ‘big’ Selmer (resp. fine Selmer) group with the specialized individual Selmer (resp. fine Selmer) groups.

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Primary Subjects: 11R23, 11F33, 11F80
Secondary Subjects: 11G05, 14G05, 16E40