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Divisor correspondences between relative schemes. (Spanish) Zbl 0578.14006

Let \(f: X\to S\) and \(g: Y\to S\) be projective cohomologically flat schemes over a scheme S of finite type over a field or over an excellent Dedekind domain. The author shows that the functor of divisorial correspondences \(T\rightsquigarrow Pic(X\times_ sY\times_ sT)/f^*(Pic(X\times_ sT)\times g^*(Pic(Y\times_ sT)\) is representable by a separated locally finitely presented and quasi-finite S-scheme of groups C(X,Y). The representabiliy of this functor follows directly from the Artin criterion. The other properties follow easily from the Néron-Severi theorem.
Reviewer: I.Dolgachev

MSC:

14C22 Picard groups
14E05 Rational and birational maps
14L15 Group schemes
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