# Brauer groups and quotient stacks

Edidin, D; Hassett, B; Kresch, A; Vistoli, A (2001). Brauer groups and quotient stacks. American Journal of Mathematics, 123(4):761-777.

## Abstract

A natural question is to determine which algebraic stacks are quotient stacks. In this paper we give some partial answers and relate it to the question of whether, for a scheme X, the natural map from the Brauer group (equivalence classes of Azumaya algebras) to the cohomological Brauer group (the torsion subgroup of $H^2(X,{\Bbb G}_m)$) is surjective.

## Abstract

A natural question is to determine which algebraic stacks are quotient stacks. In this paper we give some partial answers and relate it to the question of whether, for a scheme X, the natural map from the Brauer group (equivalence classes of Azumaya algebras) to the cohomological Brauer group (the torsion subgroup of $H^2(X,{\Bbb G}_m)$) is surjective.

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