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On the cohomology of linear groups over imaginary quadratic fields.

Dutour Sikirić, Mathieu and Gangl, Herbert and Gunnells, Paul E. and Hanke, Jonathan and Schürmann, Achill and Yasaki, Dan (2016) 'On the cohomology of linear groups over imaginary quadratic fields.', Journal of pure and applied algebra., 220 (7). pp. 2564-2589.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:04 December 2015
Date deposited:15 January 2016
Date of first online publication:19 January 2016
Date first made open access:19 January 2017

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