Noncommutative Gorenstein Projective Schemes and Gorenstein-Injective Sheaves

Abstract

We prove that if a positively-graded ring $R$ is Gorenstein and the associated torsion functor has finite cohomological dimension, then the corresponding noncommutative projective scheme $\mathrm{Tails}(R)$ is a Gorenstein category in the sense of \cite{EEG}. Moreover, under this condition, a (right) recollement relating Gorenstein-injective sheaves in $\mathrm{Tails}(R)$ and (graded) Gorenstein-injective $R$-modules is given.

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References in corpus (1)

• Gorenstein categories and Tate cohomology on projective schemes