Reference : On Farrell-Tate cohomology of SL_2 over S-integers
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/28814
On Farrell-Tate cohomology of SL_2 over S-integers
English
Rahm, Alexander mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Wendt, Matthias [Universitaet Duisburg-Essen > Mathematics]
Oct-2018
Journal of Algebra
Academic Press
512
427-464
Yes (verified by ORBilu)
International
0021-8693
1090-266X
[en] In this paper, we provide number-theoretic formulas for Farrell–Tate cohomology for SL_2 over rings of S-integers in number fields satisfying a weak regularity assumption. 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 for the Quillen conjecture,
(II) the existence of transfers for the Friedlander–Milnor conjecture,
(III) cohomology of SL_2 over number fields.
Gabor Wiese's University of Luxembourg grant AMFOR, De Brún Center for Computational Algebra at NUI Galway
Researchers ; Professionals
http://hdl.handle.net/10993/28814
10.1016/j.jalgebra.2018.06.031

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