Naslov
On the cohomology of linear groups over imaginary quadratic fields

Autori
Dutour Sikirić, Mathieu ; Gangl, Herbert ; Gunnells, Paul ; Hanke, Jonathan ; Schuermann, Achill ; Yasaki, Dan

Izvornik
Journal of pure and applied algebra (0022-4049) 220 (2016), 7; 2564-2589

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Cohomology ; Perfect form

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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