A note on the relationship between Weil and Cartier divisors

Hornell, James

doi:10.1090/S0002-9939-1975-0369360-X

A note on the relationship between Weil and Cartier divisors
HTML articles powered by AMS MathViewer

by James Hornell

Proc. Amer. Math. Soc. 48 (1975), 276-280

DOI: https://doi.org/10.1090/S0002-9939-1975-0369360-X

PDF | 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