\title[Stratifying triangulated categories]{Stratifying triangulated categories}

\keywords{localizing subcategory, thick subcategory, triangulated
category, support, local cohomology} 

\subjclass[2000]{18G99 (primary); 13D45, 18E30, 20J06, 55P42}


\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\\ 
Institut f\"ur Mathematik\\ 
Universit\"at Paderborn\\ 
33095 Paderborn\\ 
Germany.}

\begin{document}

\begin{abstract}
A notion of stratification is introduced for any compactly generated
triangulated category $\sfT$ endowed with an action of a graded
commutative noetherian ring $R$. The utility of this notion is
demonstrated by establishing diverse consequences which follow when
$\sfT$ is stratified by $R$. Among them are a classification of the
localizing subcategories of $\sfT$ in terms of subsets of the set of
prime ideals in $R$; a classification of the thick subcategories of
the subcategory of compact objects in $\sfT$; and results concerning
the support of the $R$-module of homomorphisms $\Hom_{\sfT}^{*}(C,D)$
leading to an analogue of the tensor product theorem for support
varieties of modular representation of groups.
 \end{abstract}