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arXiv · 1705.01382

Brauer groups of 1-motives

Cristiana Bertolin·Federica Galluzzi
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Abstract

Over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the group H^2_\'et(M,G_m)$ of a 1-motive M, whose pull-back via the unit section is zero, comes from an Azumaya algebra. In particular, we deduce that over an algebraically closed field of characteristic zero, all classes of H^2_\'et(M,G_m) come from Azumaya algebras.

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Cristiana Bertolin, Federica Galluzzi. 2017-05-03. Brauer groups of 1-motives. https://arxiv.org/abs/1705.01382

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