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

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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 $0$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.## References

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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