On Farrell-Tate cohomology of \(\operatorname{GL}_3\) over rings of quadratic integers

DOI10.1016/j.jalgebra.2022.09.027OpenAlexW2998885485MaRDI QIDQ2099261

Alexander D. Rahm, Matthias Wendt, Anh Tuan Bui

Publication date: 23 November 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.04277

zbMATH Keywords

cohomology of arithmetic groupsFarrell-Tate cohomologyhomological torsion\(\operatorname{GL}(3)\) over quadratic integers

Mathematics Subject Classification ID

Integral representations of finite groups (20C10) Cohomology of arithmetic groups (11F75) Orders in separable algebras (16H10) Topological (K)-theory (19Lxx)

Uses Software

• GAP
• Magma
• PARI/GP
• SageMath
• HAP

Cites Work

• Accessing the cohomology of discrete groups above their virtual cohomological dimension
• On the integral homology of \(\text{PSL}_4(\mathbb Z)\) and other arithmetic groups
• Resolutions for unit groups of orders
• Small-dimensional classifying spaces for arithmetic subgroups of general linear groups
• Integral bases for bicyclic biquadratic fields over quadratic subfields
• The Magma algebra system. I: The user language
• On Farrell-Tate cohomology of \(\mathrm{SL}_2\) over \(S\)-integers
• The Farrell-Tate and Bredon homology for \(\operatorname{PSL}_4(\mathbb{Z})\) via cell subdivisions
• A correspondence between classes of ideals and classes of matrices
• Computing in arithmetic groups with Voronoï's algorithm.
• Über Den Bizyklischen Biquadratischen Zahlkörper
• Integral Representations of Cyclic Groups of Prime Order
• On the cohomology of linear groups over imaginary quadratic fields
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