On Farrell-Tate cohomology of SL_2 over S-integers

Reference : On Farrell-Tate cohomology of SL_2 over S-integers


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/28814

Title :	On Farrell-Tate cohomology of SL_2 over S-integers
Language :	English
Author, co-author :	Rahm, Alexander [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Wendt, Matthias [Universitaet Duisburg-Essen > Mathematics]
Publication date :	Oct-2018
Journal title :	Journal of Algebra
Publisher :	Academic Press
Volume :	512
Pages :	427-464
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0021-8693
e-ISSN :	1090-266X
Abstract :	[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.
Funders :	Gabor Wiese's University of Luxembourg grant AMFOR, De Brún Center for Computational Algebra at NUI Galway
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/10993/28814
DOI :	10.1016/j.jalgebra.2018.06.031

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Open access	Rahm_and_Wendt_sl2ok_revision6.pdf		Author preprint	428.6 kB	View/Open

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