Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Ok, I found it. Even if the pair (X,Y) does not satisfy Leff, is there a way to understand when E on Y extends to a bundle on the formal completion? Some kind of obstruction perhaps to extending to various infinitesimal thickenings of Y...
Technical question: Is there an argument somewhere that the Hochschild cochain complex of the DG enhancement of the derived category of coherent sheaves has the same homotopy type as a homotopy Gerstenhaber algebra to the algebra of Dolbeault polyvector fields?
The paper in A. Bergman's comment contains the answer to my question. Indeed, the Hochschild cochain complex of a small dg category has a B-infinity structure, which is a structure that lies between the structure of a Gerstenhaber algebra and a strong homotopy Gerstenhaber algebra. According to Keller's paper, if two small dg-categories are Morita equivalent, then their Hochschild cochain complexes are isomorphic in the homotopy category of B-infinity algebras. This implies that their Hochschild cohomologies are isomorphic as Gerstenhaber algebras.
