Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
K 0 AND THE DIMENSION FILTRATION FOR p-TORSION IWASAWA MODULES
 

Summary: K 0 AND THE DIMENSION FILTRATION FOR p-TORSION
IWASAWA MODULES
KONSTANTIN ARDAKOV AND SIMON WADSLEY
Abstract. Let G be a compact p-adic analytic group. We study K-theoretic
questions related to the representation theory of the completed group algebra
kG of G with coe∆cients in a nite eld k of characteristic p. We show that
if M is a nitely generated kG-module whose dimension is smaller than the
dimension of the centralizer of any p-regular element of G, then the Euler
characteristic of M is trivial. Writing F i for the abelian category consisting of
all nitely generated kG-modules 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.

  

Source: Ardakov, Konstantin - School of Mathematical Sciences, University of Nottingham

 

Collections: Mathematics