Van den Bergh's conjecture on derived equivalence of crepant resolutions

Let $X$ be a variety admitting crepant resolutions, including commutative resolutions and non-commutative crepant resolutions. Van den Bergh's conjecture. All crepant resolutions of $X$, commutative as well as non-commutative, are derived equivalent. This extends the Bondal–Orlov–Kawamata expectation by including non-commutative crepant resolutions; the source attributes the proposal to Van den Bergh and gives no resolution of it.