In this paper, we develop the idea in [16] to obtain finer results on the structure of Selmer modules for p-adic representations than the usual main conjecture in Iwasawa theory. We determine the higher Fitting ideals of the Selmer modules under several assumptions. Especially, we describe the structure of the classical Selmer group of an elliptic curve over Q, using the ideals defined from mod...

We show that the cyclotomic conjecture on characteristic polynomial of $T$-ramified $S$-split Iwasawa modules, introduced in a previous paper and satisfied by abelian fields, governs $\mathbb Z_\ell $-rank submodule fixed points for

We prove a power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL2 over any number field that is not totally real. Our proof involves the theory of p-adically completed cohomology developed by Calegari and Emerton and a bound for the growth of coinvariants in certain finitely generated noncommutative Iwasawa modules.