K₀ and the dimension filtration for p-torsion Iwasawa modules

2006/11/01 by Konstantin Ardakov, Ardakov, Konstantin, Simon Wadsley +1
Mathematics · #11R23 #16S35 #19A31 #20C20 #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #math.KT #math.RT #msc:11R23 #msc:16S35 #msc:19A31 #msc:20C20

paper · pdf · doi:10.48550/arxiv.math/0611037

arxiv created 2006/11/01 · arxiv updated 2009/12/01

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 F_i 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 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.

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