Homological characterisation of Lambda-ranks

Abstract

If G is a pro-p, p-adic, Lie group and if $\Lambda(G)$ denotes the Iwasawa algebra of G then we present a formula for determining the $\Lambda(G)$-rank of a finitely generated $\Lambda(G)$-module. This is given in terms of the G homology groups of the module. We explore some consequences of this for the structure of $\Lambda(G)$-modules.