### Modules over Iwasawa algebras, by J. Coates, P. Schneider, R. Sujatha

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.

J. Coates, P. Schneider, R. Sujatha <J.H.Coates@dpmms.cam.ac.uk, pschnei@math.uni-muenster.de,sujatha@math.tifr.res.in>