Euler characteristics, Akashi series and compact $p$-adic Lie groups
- Autores: Simon Wadsley
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 10, 2010, págs. 3455-3465
- Idioma: inglés
- DOI: 10.1090/s0002-9939-10-10372-4
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Resumen
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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