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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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Picard and Brauer groups of Zariski schemes
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by Piotr Blass and Raymond Hoobler PDF
Proc. Amer. Math. Soc. 97 (1986), 379-383 Request permission

Abstract:

The Cartier-Yuan exact sequence is used to calculate Picard groups and Brauer groups of Zariski surfaces and their generalizations. A result of Blass-Deligne on the factoriality of general affine Zariski surfaces is extended to all higher dimensional Zariski schemes.
References
    P. Blass, Some geometric applications of a differential equation in characteristics $p > 0$ to the theory of algebraic surfaces, Contemporary Math., Vol. 13, Amer. Math. Soc., Providence, R.I., 1982.
  • Robin Hartshorne, Local cohomology, Lecture Notes in Mathematics, No. 41, Springer-Verlag, Berlin-New York, 1967. A seminar given by A. Grothendieck, Harvard University, Fall, 1961. MR 0224620
  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
  • Raymond T. Hoobler, Cohomology of purely inseparable Galois coverings, J. Reine Angew. Math. 266 (1974), 183–199. MR 364258, DOI 10.1515/crll.1974.266.183
  • —, When is ${\text {Br}}(X) = {\text {Br’}}(X)?$?, Brauer Groups in Ring Theory and Algebraic Geometry, Lecture Notes in Math., vol. 917, Springer-Verlag, New York, 1982, pp. 231-245. Milne, Étale cohomology, Princeton Math. Series, no. 33, Princeton Univ. Press, Princeton, NJ., 1980.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 379-383
  • MSC: Primary 14J05; Secondary 14F20
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0840613-9
  • MathSciNet review: 840613