One of the cornerstones in the formulation of a "Main
Conjecture" in the algebraic side of classical commutative Iwasawa theory is a
structure theorem for finitely generated modules, due to Serre/Iwasawa. In this
talk, we shall present a similar theorem for modules over non-commutative
Iwasawa algebras.
This is joint work with J. Coates and P. Schneider.
We shall also discuss further questions and some recent
developments related to this study.