 
Summary: K0 AND THE DIMENSION FILTRATION FOR pTORSION
IWASAWA MODULES
KONSTANTIN ARDAKOV AND SIMON WADSLEY
Abstract. Let G be a compact padic analytic group. We study Ktheoretic
questions related to the representation theory of the completed group algebra
kG of G with coefficients in a finite field k of characteristic p. We show that
if M is a finitely generated kGmodule whose dimension is smaller than the
dimension of the centralizer of any pregular element of G, then the Euler
characteristic of M is trivial. Writing Fi for the abelian category consisting of
all finitely generated kGmodules of dimension at most i, we provide an upper
bound for the rank of the natural map from the Grothendieck group of Fi to
that of Fd, 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.
1. Introduction
1.1. Iwasawa algebras. In this paper we study certain aspects of the representa
tion theory of Iwasawa algebras. These are the completed group algebras
G := lim

Zp[G/U],
where Zp denotes the ring of padic integers, G is a compact padic analytic
