Thick subcategories of the stable module category.
D.J. Benson, J.F. Carlson and J. Rickard.
To appear in Fundamenta Mathematicae.

\begin{abstract}
We study the thick subcategories of the stable category
of finitely generated modules for the principal block of
the  group algebra of a finite group $G$ over a field of 
characteristic $p$. In case $G$ is a $p$-group we obtain 
a complete classification of the thick subcategories. The 
same classification works whenever the nucleus of the 
cohomology variety is zero. In case the nucleus is nonzero, 
we describe some examples which lead us to believe that 
there are always infinitely many thick subcategories 
concentrated on each nonzero closed homogeneous subvariety
of the nucleus. 
\end{abstract}