Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Euler characteristics, Akashi series and compact -adic Lie groups

Author(s): Simon Wadsley
Journal: Proc. Amer. Math. Soc. 138 (2010), 3455-3465.
MSC (2010): Primary 11R23, 16U20
Posted: 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 -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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