Abstract:
Following work of Buchweitz, one defines Tate-Hochschild cohomology of
an algebra A to be the Yoneda algebra of the identity bimodule in the
singularity category of bimodules. We show *if the bounded derived
category of A is smooth* (hypothesis added on 03/06/2020) then
Tate-Hochschild cohomology is canonically isomorphic to the ordinary
Hochschild cohomology of the singularity category of A (with its
canonical dg enrichment). In joint work with Zheng Hua, we apply this to
prove a weakened version of a conjecture by Donovan-Wemyss which states
that a complete local isolated compound Du Val singularity is determined
by the derived equivalence class of the contraction algebra associated
with a smooth model.
