Asian Journal of Mathematics

Volume 16 (2012)

Number 2

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

Pages: 353 – 366

DOI: http://dx.doi.org/10.4310/AJM.2012.v16.n2.a9

Author

Somnath Jha

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.

Keywords

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

2010 Mathematics Subject Classification

Primary 11F33, 11F80, 11R23. Secondary 11G05, 14G05, 16E40.

Full Text (PDF format)