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

## TL;DR

This paper develops a theory of dg schemes as a homotopy site, establishing an equivalence of infinity categories of stacks, and shows that stacks represented by dg schemes are derived schemes, advancing derived algebraic geometry.

## Contribution

It introduces a new framework for dg schemes as a homotopy site and proves their equivalence with existing stack categories, connecting dg schemes to derived schemes.

## Key findings

- Established a homotopy site for dg schemes
- Proved the equivalence of stack categories
- Demonstrated dg scheme stacks are derived schemes

## 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 Toen 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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Source: https://tomesphere.com/paper/1908.03021