@article{19449ae47c9b43a589272b6674df57c4,
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.",
keywords = "Derived Quot scheme, Derived Quot stack, Simplicial localization",
author = "Dennis Borisov and Ludmil Katzarkov and Artan Sheshmani",
note = "Funding Information: The first author would like to thank Tony Pantev and Dingxin Zhang for very helpful conversations. The third author would like to thank Dennis Gaitsgory, Tony Pantev, Fedor Bogomolov, Roman Bezrukovnikov, Vladimir Baranovsky, Sergey Arkhipov and Alina Marian for helpful discussions and commenting on the first versions of this article. [Formula presented] The first author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [RGPIN-2020-04845]. Cette recherche a ?t? financ?e par le Conseil de Recherches en Sciences Naturelles et en G?nie du Canada (CRSNG), [RGPIN-2020-04845].The second author was partially supported by NSF Grant, Simons Investigatior Award HMS, Simons Collaboration Award HMS, National Science Fund of Bulgaria, National Scientific Program ?Excellent Research and People for the Development of European Science? (VIHREN), Project No. KP-06-DV-7, HSE University Basic Research Program.Research of third author was partially supported by generous Aarhus startup research grant of A. S., and partially by the NSF DMS-1607871, NSF DMS-1306313, the Simons 38558, and HSE University Basic Research Program. A.S. would like to further sincerely thank the Center for Mathematical Sciences and Applications at Harvard University, the Institut for Mathematik at Aarhus University, formerly known as the center for Quantum Geometry of Moduli Spaces, and the Laboratory of Mirror Symmetry in Higher School of Economics, Russian Federation, for the great help and support. Moreover the third author would like to sincerely thank help and support of Professor Shing-Tung Yau for always being there to provide crucial help, kind advice and generous support, while this project was being completed. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2022",
month = jul,
day = "16",
doi = "10.1016/j.aim.2022.108369",
language = "English (US)",
volume = "403",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}