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June 2012 Fine Selmer group of Hida deformations over non-commutative $p$-adic Lie extensions
Somnath Jha
Asian J. Math. 16(2): 353-366 (June 2012).

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.

Citation

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Somnath Jha. "Fine Selmer group of Hida deformations over non-commutative $p$-adic Lie extensions." Asian J. Math. 16 (2) 353 - 366, June 2012.

Information

Published: June 2012
First available in Project Euclid: 9 April 2012

zbMATH: 1253.11099
MathSciNet: MR2916368

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

Keywords: $p$-adic Galois representation , congruences of modular forms , Hida theory , non-commutative Iwasawa theory , Selmer group

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 2 • June 2012
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