\(S\)-arithmetic spinor groups with the same finite quotients and distinct \(\ell^2\)-cohomology
type: Item
instance of: scholarly article
title: \(S\)-arithmetic spinor groups with the same finite quotients and distinct \(\ell^2\)-cohomology
DOI: 10.4171/GGD/566
author: Holger Kammeyer
author: Roman Sauer
published in: Groups, Geometry, and Dynamics
publication date: 2021-06-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1804.10604
review text: Summary: In this note we refine examples by Aka from arithmetic to \(S\)-arithmetic groups to show that the vanishing of the \(i\)-th \(\ell^2\)-Betti number is not a profinite invariant for all \(i\geq 2\).
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 20G25
Mathematics Subject Classification ID: 11F75
zbMATH DE Number: 7357936
zbMATH Keywords: \(\ell^2\)-Betti numbers
zbMATH Keywords: profinite completion
zbMATH Keywords: \(S\)-arithmetic groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7357936