# 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.

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.

## Citations

51 citations in Web of Science®
46 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics quotient stacks; Deligne-Mumford stacks; cohomological Brauer group English 2001 29 Nov 2010 16:27 05 Apr 2016 13:25 The Johns Hopkins University Press 0002-9327 American Journal of Mathematics © 2001 The Johns Hopkins University Press https://doi.org/10.1353/ajm.2001.0024 http://www.ams.org/mathscinet-getitem?mr=1844577http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1036.14001http://www.jstor.org/stable/25099081
Permanent URL: https://doi.org/10.5167/uzh-22024