On the Noncommutative Bondal-Orlov Conjecture

Abstract

Let R be a normal, equi-codimensional Cohen-Macaulay ring of dimension $d\ge 2$ with a canonical module. We give a sufficient criterion that establishes a derived equivalence between the noncommutative crepant resolutions of R. When $d\le 3$ this criterion is always satisfied and so all noncommutative crepant resolutions of R are derived equivalent. Our method is based on cluster tilting theory for commutative algebras, developed in [IW10].

References in corpus (1)

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

Cited by in corpus (1)

• Lectures on Noncommutative Resolutions