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]**R. Hartshorne,*Local cohomology*, Lecture Notes in Math., vol. 41, Springer-Verlag, Heidelberg, 1967. MR**0224620 (37:219)****[3]**-,*Algebraic geometry*, Graduate Texts in Math., Springer-Verlag, New York, 1977. MR**0463157 (57:3116)****[4]**R. Hoobler,*Cohomology of purely inseparable Galois coverings*, J. Reine Angew. Math.**66**(1974), 183-199. MR**0364258 (51:513)****[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