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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A note on the relationship between Weil and Cartier divisors
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by James Hornell PDF
Proc. Amer. Math. Soc. 48 (1975), 276-280 Request permission

Abstract:

Using a generalized equivalence relation, a subquotient of the group of Weil divisors is shown to be isomorphic to the group of Cartier divisors modulo linear equivalence for a reduced subscheme of a projective space over a field. A difficulty of the nonreduced case is discussed.
References
  • Séminaire C. Chevalley, 3ième année: 1958/59. Variétés de Picard, École Normale Supérieure, Paris, 1960 (French). MR 0157865
  • James Hornell, Divisorial complete intersections, Pacific J. Math. 45 (1973), 217–227. MR 318119
  • Serge Lang, Abelian varieties, Interscience Tracts in Pure and Applied Mathematics, No. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1959. MR 0106225
  • David Mumford, Lectures on curves on an algebraic surface, Annals of Mathematics Studies, No. 59, Princeton University Press, Princeton, N.J., 1966. With a section by G. M. Bergman. MR 0209285
  • Maxwell Rosenlicht, Equivalence relations on algebraic curves, Ann. of Math. (2) 56 (1952), 169–191. MR 48856, DOI 10.2307/1969773
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 276-280
  • MSC: Primary 14C10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0369360-X
  • MathSciNet review: 0369360