$R$ be the Iwasawa algebra over a compact,
$G$ arises as a Galois group of number fields from Galois representations.
$M$ is a finitely generated
$R$-module. In the late 1970’s , Harris studied the
asymptotic growth of the ranks of certain coinvariants of
$M$ arising from the action
of open subgroups of
$G$ and related them to the codimension of
$M$. In this talk, we
explain how Harris’ proofs can be simplified and improved upon, with possible
applications to studying some natural subquotients of the Galois groups of number fields.