Séminaires : Séminaire d'Algèbre

Reflexivity is about a duality between two kinds of derived categories appearing in algebra and geometry. The motivating examples are the bounded derived category of a finite dimensional algebra vs its perfect complexes and the bounded derived category of a projective scheme vs its perfect complexes. In the smooth case, these categories coincide but even in the non-smooth case these two categories share some common information. In this talk I'll provide a conceptual justification for this phenomenon. The main result is a monoidal characterisation of reflexive DG-categories as introduced by Kuznetsov and Shinder. As applications of this new perspective one can prove invariance results for Hochschild cohomology, derived Picard groups and a bijection between semi-orthogonal decompositions.

This talk will take place in hybrid mode at the Institut Henri Poincaré.