Abstract

If G is a pro-p, p-adic, Lie group containing no element of order p and if Λ(G) denotes the Iwasawa algebra of G then we propose a number of invariants associated to finitely generated Λ(G)-modules, all given by various forms of Euler characteristic. The first turns out to be none other than the rank, and this gives a particularly convenient way of calculating the rank of Iwasawa modules. Others seem to play similar roles to the classical Iwasawa λ-and μ-invariants. We explore some properties and give applications to the Iwasawa theory of elliptic curves. 2000 Mathematical Subject Classification: primary 16E10; seconday 11R23.

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