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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Euler characteristics, Akashi series and compact $ p$-adic Lie groups


Author: Simon Wadsley
Journal: Proc. Amer. Math. Soc. 138 (2010), 3455-3465
MSC (2010): Primary 11R23, 16U20
Published electronically: May 5, 2010
MathSciNet review: 2661546
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Abstract: We discuss Euler characteristics for finitely generated modules over Iwasawa algebras. We show that the Euler characteristic of a module is well-defined whenever the 0th homology group is finite if and only if the relevant compact $ p$-adic Lie group is finite-by-nilpotent and that in this case all pseudo-null modules have trivial Euler characteristic. We also prove some other results relating to the triviality of Euler characteristics for pseudo-null modules as well as some analogous results for the Akashi series of Coates et al.


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Additional Information

Simon Wadsley
Affiliation: Homerton College, University of Cambridge, Cambridge, CB2 8PQ, United Kingdom
Email: S.J.Wadsley@dpmms.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10372-4
PII: S 0002-9939(10)10372-4
Keywords: Iwasawa algebra, Euler characteristic, Akashi series
Received by editor(s): December 3, 2009
Received by editor(s) in revised form: January 5, 2010
Published electronically: May 5, 2010
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.