K_0 and the dimension filtration for p-torsion Iwasawa modules

Journal article

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.

Authors: Ardakov, K; Wadsley, S

• Journal: Proceedings of the London Mathematical Society
• Volume: 97
• Issue: 1
• Pages: 31-59
• Publication date: 2006-11-01
• DOI: 10.1112/plms/pdm053
• EISSN: 1460-244X
• ISSN: 0024-6115
• Language: English
• Keywords: 11R23; 16S35; 19A31; 20C20; math.RT; math.KT