Derived moduli of schemes and sheaves

TL;DR

This paper develops a framework for derived moduli functors related to schemes and sheaves, providing conditions for their representability as derived geometric stacks, with applications to various moduli problems.

Contribution

It introduces cohomological criteria for the representability of derived moduli functors by derived geometric stacks, expanding the scope of moduli problems that can be studied in derived algebraic geometry.

Findings

Derived moduli functors can be represented by derived geometric n-stacks under certain cohomological conditions.

Examples include moduli of polarized projective varieties, vector bundles, and abelian varieties.

The paper establishes criteria for representability in the context of derived algebraic geometry.

Abstract

We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks. Examples of problems represented by derived geometric 1-stacks are derived moduli of polarised projective varieties, derived moduli of vector bundles, and derived moduli of abelian varieties.