\title[Local duality]{Local duality for representations of \\ finite group schemes}

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

\address{Dave Benson \\ 
Institute of Mathematics\\ 
University of Aberdeen\\ 
King's College\\ 
Aberdeen AB24 3UE\\ 
Scotland U.K.}

\address{Srikanth B. Iyengar\\ 
Department of Mathematics\\
University of Utah\\ 
Salt Lake City, UT 84112\\ 
U.S.A.}

\address{Henning Krause\\ 
Fakult\"at f\"ur Mathematik\\ 
Universit\"at Bielefeld\\ 
33501 Bielefeld\\ 
Germany.}

\address{Julia Pevtsova\\ 
Department of Mathematics\\ 
University of Washington\\ 
Seattle, WA 98195\\ 
U.S.A.}


\begin{document}

\begin{abstract} 
A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\fp$-local and $\fp$-torsion subcategories of the stable category, for each homogeneous prime ideal $\fp$ in the cohomology ring of the group scheme.
\end{abstract}

\keywords{Serre duality, local duality,  finite group scheme,  stable module category, Auslander-Reiten triangle}
\subjclass[2010]{16G10 (primary); 20C20, 20G10 20J06, 18E30}

\thanks{SBI was partly supported by NSF grant DMS-1503044 and JP was partly supported by NSF grants DMS-0953011 and DMS-1501146.}