\title[Local duality for Gorenstein algebras]{Local duality for the singularity category of a \\ finite
  dimensional Gorenstein algebra}

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


\begin{abstract} 
A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. 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 derived category, for each homogeneous prime ideal $\fp$ arising from the  action of a commutative ring via Hochschild cohomology.
\end{abstract}

\keywords{Gorenstein algebra, local duality, maximal Cohen-Macaulay module, Serre duality,   singulartity category}
\subjclass[2010]{16G10 (primary); 16G50, 16E65, 16E35}