Categorical resolutions of a class of derived categories

Abstract

Using the relative derived categories, we prove that if an Artin algebra $A$ has a module $T$ with ${\rm inj.dim}T<\infty$ such that $^\perp T$ is finite, then the bounded derived category $D^b({\rm mod}A)$ admits a categorical resolution; and that for CM-finite Gorenstein algebra, such a categorical resolution is weakly crepant.