Colocalizing subcategories and cosupport

David J. Benson 1 , Srikanth B. Iyengar 2 ,  and Henning Krause 3
  • 1 Institute of Mathematics, University of Aberdeen, King's 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


The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology and cosupport for triangulated categories is developed, building on earlier work of the authors on local cohomology and support.

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The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle’s Journal. In the 190 years of its existence, Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.