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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Brauer group of fibrations and symmetric products of curves
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by Georges Elencwajg PDF
Proc. Amer. Math. Soc. 94 (1985), 597-602 Request permission

Abstract:

Given a holomorphic fibering with fibre ${{\mathbf {P}}_n}$, we compare the cohomological Brauer group of the base to that of the total space. This allows us to prove that the geometric Brauer group of any symmetric product of a Riemann surface coincides with the cohomological one.
References
  • G. Elencwajg, The Brauer groups in complex geometry, Brauer groups in ring theory and algebraic geometry (Wilrijk, 1981), Lecture Notes in Math., vol. 917, Springer, Berlin-New York, 1982, pp. 222–230. MR 657432
  • G. Elencwajg and M. S. Narasimhan, Projective bundles on a complex torus, J. Reine Angew. Math. 340 (1983), 1–5. MR 691957, DOI 10.1515/crll.1983.340.1
  • Ofer Gabber, Some theorems on Azumaya algebras, The Brauer group (Sem., Les Plans-sur-Bex, 1980) Lecture Notes in Math., vol. 844, Springer, Berlin-New York, 1981, pp. 129–209. MR 611868
  • A. Grothendieck, Le groupe de Brauer. I, II, III, Dix Exposés sur la Cohomologie des Schémas, Masson, Paris, and North-Holland, Amsterdam, 1968.
  • Raymond T. Hoobler, Brauer groups of abelian schemes, Ann. Sci. École Norm. Sup. (4) 5 (1972), 45–70. MR 311664
  • I. G. Macdonald, Symmetric products of an algebraic curve, Topology 1 (1962), 319–343. MR 151460, DOI 10.1016/0040-9383(62)90019-8
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 597-602
  • MSC: Primary 32L05; Secondary 14F05
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0792268-9
  • MathSciNet review: 792268