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The resolution property for schemes and stacks

Burt Totaro
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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.

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Burt Totaro. 2002-07-23. The resolution property for schemes and stacks. https://arxiv.org/abs/math/0207210

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