Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
K0 AND THE DIMENSION FILTRATION FOR p-TORSION IWASAWA MODULES
 

Summary: K0 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 coefficients in a finite field k of characteristic p. We show that
if M is a finitely 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 Fi for the abelian category consisting of
all finitely 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 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 p-adic integers, G is a compact p-adic analytic

  

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

 

Collections: Mathematics