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Proceedings of the London Mathematical Society Advance Access published online on January 23, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdm053
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© 2007 London Mathematical Society

K0 and the dimension filtration for p-torsion Iwasawa modules

Konstantin Ardakov

University of Nottingham
University Park
Nottingham NG7 2RD
United Kingdom

Simon Wadsley

DPMMS
Centre of Mathematical Sciences
University of Cambridge
Cambridge
CB3 0WB
United Kingdom
S.J.Wadsley{at}dpmms.cam.ac.uk

Revision received 22 March 2007. Accepted 12 September 2007.

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 with canonical dimension smaller than the dimension of the centralizer, as a p-adic analytic group, 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.

2000 Mathematics Subject Classification 11R23, 16S35, 19A31, 20C20.


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