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

Wadsley, Simon

doi:10.1090/S0002-9939-10-10372-4

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