Abstract : Smooth and proper DG-categories are noncommutative versions of
smooth and proper schemes. They also include finite dimensional algebras
of finite global dimension. Kuznetsov and Shinder defined reflexive DG-categories as a (vast) generalization; they include all projective schemes
and all finite dimensional algebras. Smooth and proper DG-categories can
also be characterized as the dualizable objects in the monoidal category of
DG-categories localized at Morita equivalences. I'll explain how by using a
monoidal characterization of reflexive DG-categories, one can show that
the Hochschild cohomology of a reflexive DG-category is isomorphic to
that of its derived category of cohomologically finite modules.
