English

Invariant Brauer group of an abelian variety

Algebraic Geometry 2021-06-01 v3

Abstract

We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper bound on the rank. We exhibit many cases in which the invariant Brauer group is zero, and construct complex abelian varieties in every dimension starting with 2, both simple and non-simple, with invariant Brauer group of order 2. We also address the situation in finite characteristic and over non-closed fields.

Keywords

Cite

@article{arxiv.2007.05473,
  title  = {Invariant Brauer group of an abelian variety},
  author = {Martin Orr and Alexei N. Skorobogatov and Domenico Valloni and Yuri G. Zarhin},
  journal= {arXiv preprint arXiv:2007.05473},
  year   = {2021}
}

Comments

32 pages, to appear in Israel J. Math