On torsion in the cohomology of \(\operatorname{PSL}_2 (\mathbb Z[1/N])\)
type: Item
instance of: scholarly article
title: On torsion in the cohomology of \(\operatorname{PSL}_2 (\mathbb Z[1/N])\)
zbMATH Open document ID: 1056.11031
DOI: 10.1016/S0022-314X(02)00077-X
author: Stefan Kühnlein
published in: Journal of Number Theory
publication date: 2003-05-25T00:00:00Z
review text: Let \(p\) be a prime and let \(\Gamma\) be the \(S\)-arithmetic group \(\text{PSL}_2 (\mathbb{Z}[\frac 1p])\). Let \(X\) be the symmetric space attached to \(\Gamma\) which is a product of the upper half plane and a Bruhat-Tits tree. Let \(\partial\Gamma \setminus X\) be the boundary of the Borel-Serre compactification of \(\Gamma \setminus X\). Torsion in the group cohomology of \(\Gamma\) is known to be linked to the cohomology of \(\partial\Gamma\setminus X\). In this paper explicit calculations are done for the cohomology of \(\partial\Gamma\setminus X\) with coefficients in the Eichler-Shimura modules \(M_n\) over a field \(K\). If the characteristic of \(K\) is large enough, the author gives a list of the dimensions of the cohomology groups. To derive these, he uses an explicit description of the relevant Borel-Serre compactifications.
Mathematics Subject Classification ID: 11F75
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 1915506
zbMATH Keywords: Borel-Serre compactification
reviewed by: Anton Deitmar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915506