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Divisors on Varieties Over a Real Closed Field

Published online by Cambridge University Press:  20 November 2018

W. Kucharz
W. Kucharz*
Affiliation:
Department of Mathematics University of New Mexico Albuquerque, New Mexico 87131 U.S.A.
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Abstract

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Let X be a projective nonsingular variety over a real closed field R such that the set X(R) of R-rational points of X is nonempty. Let ClR(X) = Cl(X)/Γ(X), where Cl(X) is the group of classes of linearly equivalent divisors on X and Γ(X) is the subgroup of Cl(X) consisting of the classes of divisors whose restriction to some neighborhood of X(R) in X is linearly equivalent to 0. It is proved that the group ClR(X) is isomorphic to (Z/2)s for some non-negative integer s. Moreover, an upper bound on s is given in terms of the Z/2-dimension of the group cohomology modules of Gal(C/R), where , with values in the Néron-Severi group and the Picard variety of Xc = X xR C.

Keywords

14C2014P05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 503 - 509
Copyright
Copyright © Canadian Mathematical Society 1992

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