Singular support of categories

Abstract: In many situations, geometric objects on a space have some kind of singular support, which refines the usual support. For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections. I would like to describe a higher categorical version of this notion.

Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a 2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is the zero section, this gives the notion of categories over Z in the usual sense.

The project is motivated by the local geometric Langlands correspondence; time permitting, I hope to sketch the relation with the Langlands correspondence at the end of the talk.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar