The resolution property for schemes and stacks

Details The resolution property for schemes and stacks The resolution property for schemes and stacks

2002-07-23

arxiv.org/abs/math/0207210v1

Mathematics

Algebraic Geometry

23 pages. To appear in J. Reine Angew. Math

Scientific paper

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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