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

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 0 th homology group is finite if and only if the relevant compact p 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.