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

TY - JOUR

T1 - Shifted symplectic structures on derived Quot-stacks I – Differential graded manifolds –

AU - Borisov, Dennis

AU - Katzarkov, Ludmil

AU - Sheshmani, Artan

PY - 2022/7

Y1 - 2022/7

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

UR - http://www.scopus.com/inward/record.url?scp=85127504887&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2022.108369

DO - 10.1016/j.aim.2022.108369

M3 - Journal article

AN - SCOPUS:85127504887

SN - 0001-8708

VL - 403

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108369

ER -