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Unpublished Paper
On The Cohomology Of Linear Groups Over Imaginary Quadratic Fields
(2013)
  • Herbert Gangl
  • Paul Gunnells, University of Massachusetts - Amherst
  • Jonathan Hanke
  • Achill Schurmann
  • Mathieu Dutour Sikiric
  • Dan Yasaki
Abstract
Let 􀀀 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 􀀀 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 􀀀 up to p-power torsion for small primes p. Our main tool is the polyhedral reduction theory for 􀀀 developed by Ash [4, Ch. II] and Koecher [18]. Our results extend work of Staffeldt [29], who treated the case n = 3, D = −4. In a sequel [11] to this paper, we will apply some of these results to the computations with the K-groups K4(OD), when D = −3,−4.
Publication Date
2013
Comments
This is an unpublished paper harvested from arXiv.
Citation Information
Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schurmann, et al.. "On The Cohomology Of Linear Groups Over Imaginary Quadratic Fields" (2013)
Available at: http://works.bepress.com/paul_gunnells/45/