\title{Stratification and $\pi$-cosupport: Finite groups}

\author[Benson, Iyengar, Krause, and Pevtsova]{Dave Benson, Srikanth B. Iyengar, Henning Krause \\ and Julia Pevtsova}


\begin{abstract} 
We introduce the notion of $\pi$-cosupport as a new tool
for the stable module category of a finite group scheme.
In the case of a finite group, we use this to give a new
proof of the classification of tensor ideal localising subcategories.
In a sequel to this paper, we carry out the corresponding
classification for finite group schemes.
\end{abstract}

\keywords{cosupport, stable module category, 
finite group scheme, localising subcategory,
support, thick subcategory} \subjclass[2010]{16G10 (primary); 20C20,
20G10 20J06 (secondary)}

\date{May 24, 2015}