arXiv subjects
Publications and source records attributed to Julie Symons.
We present a general procedure for constructing triangulated categories, linear over a field, with distinct enhancements. Some of our examples can be equipped with a (non-degenerate) t-structure, thereby showing that the existence of a t-structure does not imply uniqueness of enhancements, whether in the strong or weak sense (depending on the example).
This paper provides the final ingredient in the development of the deformation theory of pretriangulated dg-categories endowed with a nice t-structure, which was initiated by the authors and is modeled after the previously developed deformation theory of abelian categories. We show how to extend a t-structure on a pretriangulated dg-category to its dg-derived category so that the Yoneda embedding becomes t-exact. We construct several equivalences between deformation problems; in particular, we prove a deformation equivalence between the bounded t-deformations of a bounded t-dg-category on the one hand, and dg-deformations of the dg-category of derived injective ind-dg-objects on the other hand. Since this latter dg-category is cohomologically concentrated in nonpositive degrees, we do not encounter curvature.