Singular support of categories
APA
Arinkin, D. (2016). Singular support of categories. Perimeter Institute. https://pirsa.org/16040075
MLA
Arinkin, Dima. Singular support of categories. Perimeter Institute, Apr. 19, 2016, https://pirsa.org/16040075
BibTex
@misc{ pirsa_PIRSA:16040075, doi = {10.48660/16040075}, url = {https://pirsa.org/16040075}, author = {Arinkin, Dima}, keywords = {Mathematical physics}, language = {en}, title = {Singular support of categories}, publisher = {Perimeter Institute}, year = {2016}, month = {apr}, note = {PIRSA:16040075 see, \url{https://pirsa.org}} }
University of Wisconsin-Milwaukee
Talk Type
Subject
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; similarly, for quasi-smooth X, the singular support of a coherent sheaf on X is a conical subset of the cohomologically shifted cotangent bundle. 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, we simply consider categories over Z in the usual sense.
This talk is based on a joint project with D.Gaitsgory. The project is motivated by the local geometric Langlands correspondence; I plan to sketch the relation with the Langlands correspondence in the talk.