Mathieu Dutour Sikirić
On the cohomology of linear groups over imaginary quadratic fields
Dutour Sikirić, Mathieu; Gangl, Herbert; Gunnells, Paul E.; Hanke, Jonathan; Schürmann, Achill; Yasaki, Dan
Authors
Professor Herbert Gangl herbert.gangl@durham.ac.uk
Professor
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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Copyright Statement
© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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