English

Brauer groups of 1-motives

Algebraic Geometry 2021-04-14 v5 Number Theory

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.

Keywords

Cite

@article{arxiv.1705.01382,
  title  = {Brauer groups of 1-motives},
  author = {Cristiana Bertolin and Federica Galluzzi},
  journal= {arXiv preprint arXiv:1705.01382},
  year   = {2021}
}

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final version