Beschreibung:
<jats:p>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<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S0027763020000021_inline1.png" /><jats:tex-math>$\mathfrak{p}$</jats:tex-math></jats:alternatives></jats:inline-formula>-local and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S0027763020000021_inline2.png" /><jats:tex-math>$\mathfrak{p}$</jats:tex-math></jats:alternatives></jats:inline-formula>-torsion subcategories of the derived category, for each homogeneous prime ideal<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S0027763020000021_inline3.png" /><jats:tex-math>$\mathfrak{p}$</jats:tex-math></jats:alternatives></jats:inline-formula>arising from the action of a commutative ring via Hochschild cohomology.</jats:p>