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 (Formula presented.) 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 (Formula presented.) Dedicated to M. Raynaud.
A note on divisorial correspondences of extensions of abelian schemes by tori
Bertolin C.
;
2020
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 (Formula presented.) 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 (Formula presented.) Dedicated to M. Raynaud.
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