Euler characteristics and compact p-adic Lie groups

Details Euler characteristics and compact p-adic Lie groups Euler characteristics and compact p-adic Lie groups

2009-09-21

arxiv.org/abs/0909.3763v2

Mathematics

Representation Theory

10 pages New material on Akashi series added; consequential restructuring done including substantial rewriting of the introduc

Scientific paper

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 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. We also prove some analogous results for the Akashi series of Coates et al.

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