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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The Picard sequences of a fibration

Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 53 (1975), 37-40
MSC: Primary 14D99
MathSciNet review: 0382275
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Abstract: A fibration, in the Zariski topology, of algebraic varieties leads to an exact sequence of cohomology of the relative units functor. Under suitable hypotheses, the exact sequence can be interpreted as a sequence including the Picard groups of the base variety, the total space, and the fibre.

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

  • [1] M. Artin, Grothendieck topologies, Mathematics Department Lecture Notes, Harvard Univ., Cambridge, Mass., 1962.
  • [2] R. Fossum and B. Iverson, On Picard groups of algebraic fibre spaces, Aarhus Universitet Matematisk Institut Preprint Series, no. 19, Aarhus, Denmark, 1972/73.

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Additional Information

PII: S 0002-9939(1975)0382275-6
Keywords: Sheaf cohomology, Leray spectral sequence, Picard group, smooth variety, rational variety
Article copyright: © Copyright 1975 American Mathematical Society