Journal of the Ramanujan Mathematical Society

Volume 30, Issue 1, March 2015 pp. 51–65.

On the homology of Iwasawa cohomology groups

Authors: Meng Fai Lim
Author institution:Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario, Canada M5S 2E4.

Summary: A fundamental observation of Iwasawa gives a criterion for a Zp[Γ]-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.

Keywords: Iwasawa cohomology groups, fine Selmer groups, S-admissible p-adic Lie extensions, Euler characteristics

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