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Let S be a locally noetherian scheme and consider two extensions G_1 and G_2of abelian S-schemes by S-tori. In this note we prove that the fppf-sheaf Corr_S(G_1,G_2) of divisorial correspondences between G_1 and G_2 is representable.Moreover, using divisorial correspondences, we show that line bundles on anextension G of an abelian scheme by a torus define group homomorphisms betweenG and Pic_{ G/S}.

A note on divisorial correspondences of extensions of abelian schemes by tori