Let S be a locally noetherian scheme and consider two extensions G1 and G2 of abelian S-schemes by S-tori. In this note we prove that the fppf-sheaf CorrS(G1,G2) of divisorial correspondences between G1 and G2 is representable. Moreover, using divisorial correspondences, we show that line bundles on an extension G of an abelian scheme by a torus define group homomorphisms between G and PicG/S.
A note on divisorial Correspondences of extensions of abelian schemes by tori
Galluzzi Federica;Bertolin Cristiana
2020-01-01
Abstract
Let S be a locally noetherian scheme and consider two extensions G1 and G2 of abelian S-schemes by S-tori. In this note we prove that the fppf-sheaf CorrS(G1,G2) of divisorial correspondences between G1 and G2 is representable. Moreover, using divisorial correspondences, we show that line bundles on an extension G of an abelian scheme by a torus define group homomorphisms between G and PicG/S.
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