 
Summary: K 0 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 coeÆcients in a nite eld k of characteristic p. We show that
if M is a nitely 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 F i for the abelian category consisting of
all nitely generated kGmodules of dimension at most i, we provide an upper
bound for the rank of the natural map from the Grothendieck group of F i to
that of F 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.
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
Z p [G=U ];
where Z p denotes the ring of p adic integers, G is a compact p adic analytic
group, and the inverse limit is taken over the open normal subgroups U of G.
