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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Euler characteristics, Akashi series and compact $p$-adic Lie groups
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by Simon Wadsley PDF
Proc. Amer. Math. Soc. 138 (2010), 3455-3465 Request permission

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 $0$th 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
  • MR Author ID: 770243
  • Email: S.J.Wadsley@dpmms.cam.ac.uk
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3455-3465
  • MSC (2010): Primary 11R23, 16U20
  • DOI: https://doi.org/10.1090/S0002-9939-10-10372-4
  • MathSciNet review: 2661546