Non-commutative resolutions and Grothendieck groups

Abstract

Let $R$ be a noetherian normal domain. We investigate when $R$ admits a faithful module whose endomorphism ring has finite global dimension. This can be viewed as a non-commutative desingularization of $\Spec(R)$. We show that the existence of such modules forces stringent conditions on the Grothendieck group of finitely generated modules over $R$. In some cases those conditions are enough to imply that $\Spec(R)$ has only rational singularities.

Final version, to appear in Journal of Noncommutative Geometry

References in corpus (1)

• Maximal Modifications and Auslander-Reiten Duality for Non-isolated Singularities

Cited by in corpus (1)

• Annihilation of cohomology and strong generation of module categories