Modules over Iwasawa algebras

Abstract

Let G be a compact p-adic Lie group, and let Lambda(G) be its Iwasawa algebra. The present paper establishes results about the structure theory of finitely generated torsion Lambda(G)-modules, up to pseudo-isomorphism, which are largely parallel to the classical theory when G is abelian (except for basic differences which occur for those torsion modules which do not possess a non-zero global annihilator). We illustrate our general theory by concrete examples of such modules arising from the Iwasawa theory of elliptic curves without complex multiplication over the field generated by all of their p-power torsion points.