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Brauer groups and quotient stacks

D. Edidin·B. Hassett·A. Kresch·A. Vistoli
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Abstract

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

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D. Edidin, B. Hassett, A. Kresch, A. Vistoli. 2001-02-12. Brauer groups and quotient stacks. https://arxiv.org/abs/math/9905049

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