2009/09/21 by Simon Wadsley, Wadsley, Simon
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.0909.3763
10 pages New material on Akashi series added; consequential restructuring done including substantial rewriting of the introduction
arxiv created 2009/10/08 · arxiv updated 2009/12/01
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.