Hernández Ruipérez, Daniel Divisor correspondences between relative schemes. (Spanish) Zbl 0578.14006 Rev. Mat. Hisp.-Am., IV. Ser. 41, 151-167 (1981). 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 Keywords:Picard scheme; functor of divisorial correspondences; representabiliy PDFBibTeX XMLCite \textit{D. Hernández Ruipérez}, Rev. Mat. Hisp.-Am., IV. Ser. 41, 151--167 (1981; Zbl 0578.14006)