\title[Colocalizing subcategories and cosupport]
{Colocalizing subcategories and cosupport}

\author{Dave Benson} 
\address{Dave Benson \\ 
Institute of Mathematics\\ 
University of Aberdeen\\ 
King's College\\ 
Aberdeen AB24 3UE\\ 
Scotland U.K.}

\author{Srikanth B. Iyengar} 
\address{Srikanth B. Iyengar\\ 
Department of Mathematics\\ 
University of Nebraska\\ 
Lincoln, NE 68588\\ 
U.S.A.}

\author{Henning Krause} 
\address{Henning Krause\\ 
Fakult\"at f\"ur Mathematik\\ 
Universit\"at Bielefeld\\ 
33501 Bielefeld\\ 
Germany.}


\begin{document}

\begin{abstract}
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.
\end{abstract}

\keywords{colocalizing subcategory, cosupport, local homology, 
localizing subcategory, stable module category, triangulated category}

\subjclass[2010]{20J06(primary); 13D45, 16E45, 18E30}

\thanks{The research of the first and second authors was undertaken
  during visits to the University of Paderborn, each supported by a
  research prize from the Humboldt Foundation. The research of the
  second author was also partly supported by NSF grant DMS 0903493.}