\title[Module categories for group algebras]{Module categories for
  group algebras \\ over commutative rings}

\author[Benson, Iyengar, Krause]{Dave Benson, Srikanth B. Iyengar, Henning Krause\\
with an appendix by Greg Stevenson}

\begin{abstract} We develop a suitable version of the stable module
category of a finite group $G$ over an arbitrary commutative ring $k$.
The purpose of the construction is to produce a compactly generated
triangulated category whose compact objects are the finitely presented
$kG$-modules.  The main idea is to form a localisation of the usual
version of the stable module category with respect to the filtered
colimits of weakly injective modules. There is also an analogous
version of the homotopy category of weakly injective $kG$-modules and
a recollement relating the stable category, the homotopy category, and
the derived category of $kG$-modules.
\end{abstract}