Modules over Iwasawa algebras

Abstract

Let $p$ be a prime number, and $G$ a compact $p$-adic Lie group. We recall that the Iwasawa algebra $\Lambda(G)$ is defined to be the completed group ring of $G$ over the ring of $p$-adic integers. Interesting examples of finitely generated modules over $\Lambda(G),$ in which $G$ is the image of Galois in the automorphism group of a $p$-adic Galois representation, abound in arithmetic geometry. The study of such $\Lambda(G)$-modules arising from arithmetic geometry can be thought of as a natural generalization of Iwasawa theory. One of the cornerstones of classical Iwasawa theory is the fact that, when $G$ is the additive group of $p$-adic integers, a good structure theory for finitely generated $\Lambda(G)$-modules is known, up to pseudo-isomorphism. The aim of the present paper is to extend as much as possible of this commutative structure theory to the non-commuta tive case.