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PIRSA:23030106

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https://pirsa.org/23030106

Decategorifying the singular support of coherent sheaves

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

Kendric Schefers The University of Texas at Austin

Talk numberPIRSA:23030106
DOI10.48660/23030106
Source RepositoryPIRSA
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Talk Type Scientific Series
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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