Abstract: | Let G be a compact p-adic analytic group. We study K-theoreticquestions related to the representation theory of the completedgroup algebra kG of G with coefficients in a finite field kof characteristic p. We show that if M is a finitely generatedkG-module with canonical dimension smaller than the dimensionof the centralizer, as a p-adic analytic group, of any p-regularelement of G, then the Euler characteristic of M is trivial.Writing i for the abelian category consisting of all finitelygenerated kG-modules of dimension at most i, we provide an upperbound for the rank of the natural map from the Grothendieckgroup of i to that of d, where d denotes the dimension of G.We show that this upper bound is attained in some special cases,but is not attained in general. |