Derived equivalence of crepant resolutions and noncommutative crepant resolutions

Let $R$ be an equidimensional normal Gorenstein ring. A noncommutative crepant resolution of $R$ is an endomorphism ring of a modifying $R$-module with finite global dimension, while a crepant resolution is a crepant resolution of the singularity $d4cSpec R$. Derived equivalence conjecture. All crepant resolutions and all noncommutative crepant resolutions of $R$ should be derived equivalent. This is a central problem in the study of noncommutative crepant resolutions; the statement concerns whether the commutative and noncommutative crepant models associated with the same ring have equivalent derived categories.