Number Theory Seminar

Title: Conservative descent for semi-orthogonal decompositions

Speaker: Daniel Bergh

Abstract:
Semi-orthogonal decompositions arise naturally in many situations in the study of derived categories in algebraic geometry. For instance, there are naturally associated semi-orthogonal decompositions of the derived categories of blow-ups, projective bundles, Brauer-Severi schemes, gerbes and root stacks.

I will give a brief introduction to the subject. I will also present some ongoing work (joint with Olaf Schnürer) on how to construct semi-orthogonal decompositions locally, using a technique we call conservative descent. In particular, this allows us to prove existence of the semi-orthogonal decompositions for the geometric constructions mentioned above to the more general context of algebraic stacks, as well as remove some regularity and finiteness assumptions.