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arXiv · 1902.07448

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

Cristiana Bertolin·Federica Galluzzi
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Abstract

Let S be a locally noetherian scheme and consider two extensions G_1 and G_2 of 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 an extension G of an abelian scheme by a torus define group homomorphisms between G and Pic_{ G/S}.

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Cristiana Bertolin, Federica Galluzzi. 2019-02-20. A note on divisorial correspondences of extensions of abelian schemes by tori. https://arxiv.org/abs/1902.07448

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