Invariant Brauer group of an abelian variety

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Authors

  • Martin Orr
  • Alexei N. Skorobogatov
  • Domenico Valloni
  • Yuri G. Zarhin

Research Organisations

External Research Organisations

  • University of Manchester
  • Imperial College London
  • Russian Academy of Sciences (RAS)
  • Pennsylvania State University
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Details

Original languageEnglish
Pages (from-to)695-733
Number of pages39
JournalIsrael journal of mathematics
Volume249
Issue number2
Early online date29 Jun 2022
Publication statusPublished - Jun 2022

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.

ASJC Scopus subject areas

Cite this

Invariant Brauer group of an abelian variety. / Orr, Martin; Skorobogatov, Alexei N.; Valloni, Domenico et al.
In: Israel journal of mathematics, Vol. 249, No. 2, 06.2022, p. 695-733.

Research output: Contribution to journal › Article › Research › peer review

Orr M, Skorobogatov AN, Valloni D, Zarhin YG. Invariant Brauer group of an abelian variety. Israel journal of mathematics. 2022 Jun;249(2):695-733. Epub 2022 Jun 29. doi: 10.48550/arXiv.2007.05473, 10.1007/s11856-022-2323-5
Orr, Martin ; Skorobogatov, Alexei N. ; Valloni, Domenico et al. / Invariant Brauer group of an abelian variety. In: Israel journal of mathematics. 2022 ; Vol. 249, No. 2. pp. 695-733.
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