engleski

On the cohomology of linear groups over imaginary quadratic fields

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.

Cohomology ; Perfect form

nije evidentirano