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On the cohomology of linear groups over imaginary quadratic fields

Dutour Sikirić, Mathieu; Gangl, Herbert; Gunnells, Paul E.; Hanke, Jonathan; Schürmann, Achill; Yasaki, Dan

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Authors

Mathieu Dutour Sikirić

Paul E. Gunnells

Jonathan Hanke

Achill Schürmann

Dan Yasaki



Abstract

Let Γ be the group GLN(OD), where OD is the ring of integers in the imaginary quadratic field with discriminant D<0. In this paper we investigate the cohomology of Γ for N=3,4 and for a selection of discriminants: D≥−24 when N=3, and D=−3,−4 when N=4. In particular we compute the integral cohomology of Γ up to p-power torsion for small primes p. Our main tool is the polyhedral reduction theory for Γ developed by Ash [4, Ch. II] and Koecher [24]. Our results extend work of Staffeldt [40], who treated the case N=3, D=−4. In a sequel [15] to this paper, we will apply some of these results to computations with the K -groups K4(OD), when D=−3,−4.

Citation

Dutour Sikirić, M., Gangl, H., Gunnells, P. E., Hanke, J., Schürmann, A., & Yasaki, D. (2016). On the cohomology of linear groups over imaginary quadratic fields. Journal of Pure and Applied Algebra, 220(7), 2564-2589. https://doi.org/10.1016/j.jpaa.2015.12.002

Journal Article Type Article
Acceptance Date Dec 4, 2015
Online Publication Date Jan 19, 2016
Publication Date Jul 1, 2016
Deposit Date Dec 14, 2015
Publicly Available Date Mar 29, 2024
Journal Journal of Pure and Applied Algebra
Print ISSN 0022-4049
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 220
Issue 7
Pages 2564-2589
DOI https://doi.org/10.1016/j.jpaa.2015.12.002

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