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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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:quotient stacks; Deligne-Mumford stacks; cohomological Brauer group
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:06 Dec 2017 20:52
Publisher:The Johns Hopkins University Press
ISSN:0002-9327
Additional Information:American Journal of Mathematics © 2001 The Johns Hopkins University Press
Publisher DOI:https://doi.org/10.1353/ajm.2001.0024
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1844577
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1036.14001
http://www.jstor.org/stable/25099081

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