Comptes Rendus
no. 17-18
Algebra/Homological Algebra
Localising subcategories for cochains on the classifying space of a finite group
[Sous-catégories localisantes pour les co-chaînes des espaces classifiants de groupes finis]

Présenté par : the Editorial Board

Dave Benson1 ; Srikanth B. Iyengar2 ; Henning Krause3
1 Institute of Mathematics, University of Aberdeen, Kingʼs College, Aberdeen AB24 3UE, Scotland, UK
2 Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA
3 Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 953-956.

Nous identifions les sous-catégories localisantes de la catégorie dérivée des co-chaînes, à coefficients dans un corps k de caractéristique p, sur lʼespace classifiant dʼun groupe fini G. Elles sont en correspondance biunivoque avec les sous-ensembles de lʼensemble des idéaux premiers homogènes de lʼanneau de co-homologie H⁎(G,k).

The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology ring H⁎(G,k).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.019
Dave Benson 1 ; Srikanth B. Iyengar 2 ; Henning Krause 3

1 Institute of Mathematics, University of Aberdeen, Kingʼs College, Aberdeen AB24 3UE, Scotland, UK
2 Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA
3 Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany 
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Dave Benson; Srikanth B. Iyengar; Henning Krause. Localising subcategories for cochains on the classifying space of a finite group. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 953-956. doi : 10.1016/j.crma.2011.08.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.019/

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[7] J.F. Carlson The thick subcategory generated by the trivial module, Bielefeld, 1998 (Trends in Mathematics), Birkhäuser, Basel (2000), pp. 285-296

[8] A.D. Elmendorf; I. Kříž; M.A. Mandell; J.P. May Rings, Modules and Algebras in Stable Homotopy Theory, Surveys and Monographs, vol. 47, American Mathematical Society, 1996

[9] H. Krause The stable derived category of a Noetherian scheme, Compos. Math., Volume 141 (2005), pp. 1128-1162

[10] G. Stevenson Support theory via actions of tensor triangulated categories | arXiv

Cité par Sources :

☆ The research of the second author was undertaken during a visit to the University of Bielefeld, supported by a research prize from the Humboldt Foundation, and by NSF grant DMS 0903493.

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