On Farrell-Tate cohomology of SL_2 over S-integers

Alexander D. Rahm (1) , Matthias Wendt (2)

1 NUIG - Department of Mathematics
2 Fakultät für Mathematik der Universität Duisburg-Essen

In this paper, we provide number-theoretic formulas for Farrell-Tate cohomology for SL_2 over rings of S-integers in number fields. These formulas describe group cohomology above the virtual cohomological dimension, and can be used to study some questions in homology of linear groups. We expose three applications: to (I) detection questions, (II) the existence of transfers, (III) cohomology of SL_2 over number fields.

Mots clés: Farrell-Tate cohomology; S-arithmetic groups; group homology

Domaines: K-théorie et homologie [math.KT]

Alexander D. Rahm, Matthias Wendt. On Farrell-Tate cohomology of SL_2 over S-integers. 2014. ⟨hal-01081081v1⟩