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

DOI:
https://doi.org/10.1090/S0002-9939-1986-0840613-9

MathSciNet review:
840613

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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.

**[1]**P. Blass,*Some geometric applications of a differential equation in characteristics**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****[3]**Robin Hartshorne,*Algebraic geometry*, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR**0463157****[4]**Raymond T. Hoobler,*Cohomology of purely inseparable Galois coverings*, J. Reine Angew. Math.**266**(1974), 183–199. MR**0364258**, https://doi.org/10.1515/crll.1974.266.183**[5]**-,*When is*?, 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.

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0840613-9

Article copyright:
© Copyright 1986
American Mathematical Society