PIRSA:16040075 Conference Mathematical physics

DOI10.48660/16040075

Conference/School: Deformation Quantization of Shifted Poisson Structures

Arinkin, D. (2016). Singular support of categories. Perimeter Institute. https://pirsa.org/16040075

Arinkin, Dima. Singular support of categories. Perimeter Institute, Apr. 19, 2016, https://pirsa.org/16040075 

@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}}
}

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.

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