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Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry

Paul Balmer, Ivo Dell’Ambrogio and Beren Sanders

Algebraic & Geometric Topology 15 (2015) 3023–3045
Abstract

For equivariant stable homotopy theory, equivariant KK–theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative separable extension, analogous to finite étale extensions in algebraic geometry.

Keywords
Restriction, equivariant triangulated categories, separable, étale
Mathematical Subject Classification 2010
Primary: 13B40, 18E30
Secondary: 55P91, 19K35, 14F05
References
Publication
Received: 11 November 2014
Revised: 9 February 2015
Accepted: 9 February 2015
Published: 10 December 2015
Authors
Paul Balmer
Mathematics Department
University of California, Los Angeles
Los Angeles, CA 90095-1555
USA
http://www.math.ucla.edu/~balmer
Ivo Dell’Ambrogio
Laboratoire de Mathématiques Paul Painlevé
Université de Lille 1
F-59665 Villeneuve-d’Ascq Cedex
France
http://math.univ-lille1.fr/~dellambr/
Beren Sanders
Centre for Symmetry and Deformation
Institut for Matematiske Fag
Universitetsparken 5
DK-2100 Copenhagen
Denmark
http://beren.blogs.ku.dk/