Uniqueness of dg enhancements in geometric contexts

It was a general belief and a formal conjecture by Bondal, Larsen and Lunts
that the dg enhancement of the bounded derived category of coherent
sheaves or the category of perfect complexes on a (quasi-)projective
scheme is unique. This was proved by Lunts and Orlov in a seminal
paper. In this talk we will explain how to extend Lunts-Orlov's
results to several interesting geometric contexts. Namely, we care
about the category of perfect complexes on noetherian separated
schemes with enough locally free sheaves and the derived category of
quasi-coherent sheaves on any scheme. These results will be compared to the
existence and uniqueness of dg lifts of exact functors of geometric nature.
This is a joint work with A. Canonaco.

Contact person: Lidia Angeleri