Asian Journal of Mathematics
Volume 16 (2012)
Fine Selmer group of Hida deformations over non-commutative $p$-adic Lie extensions
Pages: 353 – 366
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.
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.