Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Picard and Brauer groups of Zariski schemes


Authors: Piotr Blass and Raymond Hoobler
Journal: Proc. Amer. Math. Soc. 97 (1986), 379-383
MSC: Primary 14J05; Secondary 14F20
MathSciNet review: 840613
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] Robin Hartshorne, Local cohomology, A seminar given by A. Grothendieck, Harvard University, Fall, vol. 1961, Springer-Verlag, Berlin-New York, 1967. MR 0224620 (37 #219)
  • [3] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157 (57 #3116)
  • [4] Raymond T. Hoobler, Cohomology of purely inseparable Galois coverings, J. Reine Angew. Math. 266 (1974), 183–199. MR 0364258 (51 #513)
  • [5] -, 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.
  • [6] Milne, Étale cohomology, Princeton Math. Series, no. 33, Princeton Univ. Press, Princeton, NJ., 1980.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14J05, 14F20

Retrieve articles in all journals with MSC: 14J05, 14F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0840613-9
PII: S 0002-9939(1986)0840613-9
Article copyright: © Copyright 1986 American Mathematical Society