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.
2020
48
7
3030
3034
https://doi.org/10.1080/00927872.2020.1726941
Group schemes, divisorial correspondences
Galluzzi Federica, Bertolin Cristiana
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1729741
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