\title{Idempotent $kG$-modules with injective cohomology}
\author{Dave Benson}
\address{Department of Mathematics, University of Aberdeen,
Aberdeen AB24 3EA, Scotland, UK}
\thanks{This research was partly supported by a senior scientist prize 
from the Humboldt foundation}

\begin{abstract}
Let $G$ be a finite group and $k$ a field of characteristic $p$.
This paper gives a short proof of a recent theorem of Benson
and Greenlees, stating that the cohomology of the kappa module $\kappa_\p$
of Benson, Carlson and Rickard is equal to the injective hull of
$H^*(G,k)/\p$ as a graded $H^*(G,k)$-module. This shorter proof does not
naturally extend to compact Lie groups, whereas the version of Benson and
Greenlees is proved in this broader context.
\end{abstract}