On the Homology of Iwasawa Cohomology Groups

Abstract

A fundamental observation of Iwasawa gives a criterion for a Zp[q-module to be torsion. In this paper, we study and prove a certain extension of this criterion which will be applied to investigate the structure of the homology of the "Iwasawa cohomology groups" of a Galois module over a p-adic Lie extension. Namely, we will answer partially a question of Hachimori on the structure of the homology of the first Iwasawa cohomology groups as modules over Iwasawa algebras and study the pseudo-nullity of the homology of the second Iwasawa cohomology groups and dual fine Selmer groups.