Shifted symplectic structures on derived Quot-stacks I – Differential graded manifolds –

Dennis Borisov; Ludmil Katzarkov; Artan Sheshmani

doi:10.1016/j.aim.2022.108369

Shifted symplectic structures on derived Quot-stacks I – Differential graded manifolds –

Dennis Borisov, Ludmil Katzarkov, Artan Sheshmani^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

2 Citations (Scopus)

Abstract

A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by Toën and Vezzosi, on the site of dg algebras whose cohomologies have finitely many generators in each degree. Stacks represented by dg schemes are shown to be derived schemes under this correspondence.

Original language	English
Article number	108369
Journal	Advances in Mathematics
Volume	403
Number of pages	31
ISSN	0001-8708
DOIs	https://doi.org/10.1016/j.aim.2022.108369
Publication status	Published - Jul 2022

Keywords

Derived Quot scheme
Derived Quot stack
Simplicial localization

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10.1016/j.aim.2022.108369

https://arxiv.org/pdf/1908.03021.pdf

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title = "Shifted symplectic structures on derived Quot-stacks I – Differential graded manifolds –",

abstract = "A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by To{\"e}n and Vezzosi, on the site of dg algebras whose cohomologies have finitely many generators in each degree. Stacks represented by dg schemes are shown to be derived schemes under this correspondence.",

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N2 - A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by Toën and Vezzosi, on the site of dg algebras whose cohomologies have finitely many generators in each degree. Stacks represented by dg schemes are shown to be derived schemes under this correspondence.

AB - A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by Toën and Vezzosi, on the site of dg algebras whose cohomologies have finitely many generators in each degree. Stacks represented by dg schemes are shown to be derived schemes under this correspondence.

KW - Derived Quot scheme

KW - Derived Quot stack

KW - Simplicial localization

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DO - 10.1016/j.aim.2022.108369

M3 - Journal article

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Shifted symplectic structures on derived Quot-stacks I – Differential graded manifolds –

Abstract

Keywords

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