Geodesic
Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry
Balmer, Paul1 ; Dell’Ambrogio, Ivo2 ; Sanders, Beren3
1Mathematics Department, University of California, Los Angeles, Los Angeles, CA 90095-1555, USA
2Laboratoire de Mathématiques Paul Painlevé, Université de Lille 1, F-59665 Villeneuve-d’Ascq Cedex, France
3Centre for Symmetry and Deformation, Institut for Matematiske Fag, Universitetsparken 5, DK-2100 Copenhagen, Denmark
Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 3023-3045
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2015.15.3025
Classification : 13B40, 18E30, 55P91, 19K35, 14F05
Keywords: Restriction, equivariant triangulated categories, separable, étale

Balmer, Paul  1   ; Dell’Ambrogio, Ivo  2   ; Sanders, Beren  3

1 Mathematics Department, University of California, Los Angeles, Los Angeles, CA 90095-1555, USA
2 Laboratoire de Mathématiques Paul Painlevé, Université de Lille 1, F-59665 Villeneuve-d’Ascq Cedex, France
3 Centre for Symmetry and Deformation, Institut for Matematiske Fag, Universitetsparken 5, DK-2100 Copenhagen, Denmark 
@article{10_2140_agt_2015_15_3025,
     author = {Balmer, Paul and Dell{\textquoteright}Ambrogio, Ivo and Sanders, Beren},
     title = {Restriction to finite-index subgroups as \'etale extensions in topology, {KK{\textendash}theory} and geometry},
     journal = {Algebraic and Geometric Topology},
     pages = {3023--3045},
     year = {2015},
     volume = {15},
     number = {5},
     doi = {10.2140/agt.2015.15.3025},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.3025/}
}
TY  - JOUR
AU  - Balmer, Paul
AU  - Dell’Ambrogio, Ivo
AU  - Sanders, Beren
TI  - Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry
JO  - Algebraic and Geometric Topology
PY  - 2015
SP  - 3023
EP  - 3045
VL  - 15
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.3025/
DO  - 10.2140/agt.2015.15.3025
ID  - 10_2140_agt_2015_15_3025
ER  - 
%0 Journal Article
%A Balmer, Paul
%A Dell’Ambrogio, Ivo
%A Sanders, Beren
%T Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry
%J Algebraic and Geometric Topology
%D 2015
%P 3023-3045
%V 15
%N 5
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.3025/
%R 10.2140/agt.2015.15.3025
%F 10_2140_agt_2015_15_3025
Balmer, Paul; Dell’Ambrogio, Ivo; Sanders, Beren. Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry. Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 3023-3045. doi: 10.2140/agt.2015.15.3025

[1] P Balmer, Separability and triangulated categories, Adv. Math. 226 (2011) 4352

[2] P Balmer, Separable extensions in tensor-triangular geometry and generalized Quillen stratification, preprint (2013)

[3] P Balmer, Stacks of group representations, J. Eur. Math. Soc. $($JEMS$)$ 17 (2015) 189

[4] J Bernstein, V Lunts, Equivariant sheaves and functors, Lecture Notes in Mathematics 1578, Springer (1994)

[5] G Cortiñas, E Ellis, Isomorphism conjectures with proper coefficients, J. Pure Appl. Algebra 218 (2014) 1224

[6] H Fausk, P Hu, J P May, Isomorphisms between left and right adjoints, Theory Appl. Categ. 11 (2003) 107

[7] E Guentner, N Higson, J Trout, Equivariant $E$–theory for $C^*$–algebras, Mem. Amer. Math. Soc. 703, Amer. Math. Soc. (2000)

[8] P S Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs 99, Amer. Math. Soc. (2003)

[9] G Lewis, J P May, J Mcclure, Ordinary $RO(G)$–graded cohomology, Bull. Amer. Math. Soc. 4 (1981) 208

[10] L G Lewis Jr., J P May, M Steinberger, J E Mcclure, Equivariant stable homotopy theory, Lecture Notes in Mathematics 1213, Springer (1986)

[11] J P May, Equivariant homotopy and cohomology theory, CBMS Regional Conference Series in Mathematics 91, Amer. Math. Soc. (1996)

[12] J P May, The Wirthmüller isomorphism revisited, Theory Appl. Categ. 11 (2003) 132

[13] R Meyer, Equivariant Kasparov theory and generalized homomorphisms, $K$–Theory 21 (2000) 201

[14] R Meyer, Categorical aspects of bivariant $K$–theory, from: "$K$–theory and noncommutative geometry" (editors G Cortiñas, J Cuntz, M Karoubi, R Nest, C A Weibel), Eur. Math. Soc. (2008) 1

[15] R Meyer, Universal coefficient theorems and assembly maps in $\mathit{KK}$–theory, from: "Topics in algebraic and topological $K$–theory", Lecture Notes in Math. 2008, Springer (2011) 45

[16] R Meyer, R Nest, The Baum–Connes conjecture via localisation of categories, Topology 45 (2006) 209

[17] P F Dos Santos, A note on the equivariant Dold–Thom theorem, J. Pure Appl. Algebra 183 (2003) 299

[18] P F Dos Santos, Z Nie, A model for equivariant Eilenberg–Mac Lane spectra,

Cité par Sources :