\title{Stratifying the derived category of cochains on $BG$ for $G$ a compact
  Lie group}
\author{Dave Benson}
\address{Institute of Mathematics, University of Aberdeen, Aberdeen
  AB24 3UE, UK}
\author{John Greenlees}
\address{School of Mathematics and Statistics, University of Sheffield,
Hicks Building, Sheffield S3 7RH, UK}
\begin{document}
\begin{abstract}
The main purpose of this paper is to classify the localising
subcategories of the derived category $\sfD(C^*(BG;k))$ where
$G$ is a compact Lie group and $k$ is a field. We also prove
a version of Chouinard's theorem for $\sfD(C^*(BG;k))$, 
we describe the relationship between induction and coinduction 
for a closed subgroup of $G$, and we use this to describe the relationship
between Hochschild homology and cohomology of $C^*(BG;k)$.
\end{abstract}