The resolution property for schemes and stacks

TL;DR

This paper establishes the equivalence of two key properties of algebraic stacks, including the resolution property, and applies these results to orbifolds with associated schemes, advancing understanding in algebraic geometry.

Contribution

It proves the equivalence of being a quotient stack and the resolution property for algebraic stacks, including orbifolds with scheme-associated algebraic spaces.

Findings

Equivalence of quotient stack and resolution property for algebraic stacks

Validation of these properties for orbifolds with scheme-associated algebraic spaces

Advancement in understanding the structure of algebraic stacks and orbifolds

Abstract

We prove the equivalence of two fundamental properties of algebraic stacks: being a quotient stack in a strong sense, and the resolution property, which says that every coherent sheaf is a quotient of some vector bundle. Moreover, we prove these properties in the important special case of orbifolds whose associated algebraic space is a scheme.