# Decategorifying the singular support of coherent sheaves

### APA

Schefers, K. (2023). Decategorifying the singular support of coherent sheaves. Perimeter Institute. https://pirsa.org/23030106

### MLA

Schefers, Kendric. Decategorifying the singular support of coherent sheaves. Perimeter Institute, Mar. 31, 2023, https://pirsa.org/23030106

### BibTex

@misc{ pirsa_PIRSA:23030106, doi = {10.48660/23030106}, url = {https://pirsa.org/23030106}, author = {Schefers, Kendric}, keywords = {Mathematical physics}, language = {en}, title = {Decategorifying the singular support of coherent sheaves}, publisher = {Perimeter Institute}, year = {2023}, month = {mar}, note = {PIRSA:23030106 see, \url{https://pirsa.org}} }

Kendric Schefers The University of Texas at Austin

## Abstract

On smooth schemes, every coherent sheaf admits a finite resolution by vector bundles, but on singular schemes, this is no longer true. The Arinkin-Gaitsgory singular support of coherent sheaves is an invariant of coherent sheaves on certain singular spaces that measures how far a particular coherent sheaf is from having such a resolution. In this talk, I will explain how the Arinkin-Gaitsgory theory of singular support decategorifies to a notion of singular support for chains on the associated complex analytic space of our scheme, measuring the difference between cohomology and Borel-Moore homology on singular spaces. In order to do so, we take advantage of the relationship between coherent sheaves and certain categories of matrix factorizations, also know as D-branes in Landau-Ginzburg models.

Zoom link: https://pitp.zoom.us/j/95698955865?pwd=Rm9ld3FUK3hiWGUzenBuZnQyTTRYZz09