  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
$\mathfrak{p}$-local and $\mathfrak{p}$-torsion subcategories of the derived
category, for each homogeneous prime ideal $\mathfrak{p}$ arising from the
action of a commutative ring via Hochschild cohomology.
