Singular Hochschild cohomology via the singularity category (1809.05121v10)

Abstract: We show that for a noetherian algebra $A$ whose bounded dg derived category is smooth, the singular Hochschild cohomology (=Tate--Hochschild cohomology) is isomorphic, as a graded algebra, to the Hochschild cohomology of the dg singularity category of $A$. The existence of such an isomorphism is suggested by recent work of Zhengfang Wang.