Cohomology and intersection theory on stacks

Abstract: I will give an overview of some recent work on extending cohomological and intersection-theoretic methods to stacks. This formalism subsumes equivariant intersection theory in the sense of Edidin-Graham and also incorporates virtual phenomena via a derived version of specialization to the normal cone. I will also discuss a very general new localization theorem for stacks which recovers Atiyah-Bott localization in the case of quotients by torus actions. Finally, I will explain a categorification of this story, involving a derived microlocalization functor for constructible sheaves, which is closely connected with categorified Donaldson-Thomas theory. The localization theorem is joint with Aranha, Latyntsev, Park and Ravi, and the applications to DT theory are joint with Kinjo.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar