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A note on the rational homological dimension of lattices in positive characteristic

Part of: Connections with homological algebra and category theory Special aspects of infinite or finite groups

Published online by Cambridge University Press:  10 June 2022

Sam Hughes Open the ORCID record for Sam Hughes [Opens in a new window]
Sam Hughes*
Affiliation:
Mathematical Institute, Andrew Wiles Building, University of Oxford, Oxford OX2 6GG, UK E-mail: sam.hughes@maths.ox.ac.uk
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Abstract

We show via $\ell^2$ -homology that the rational homological dimension of a lattice in a product of simple simply connected Chevalley groups over global function fields is equal to the rational cohomological dimension and to the dimension of the associated Bruhat–Tits building.

MSC classification

Primary: 20J06: Cohomology of groups
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 1 , January 2023 , pp. 138 - 140
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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