Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4

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

Authors

  • Vladimir Mitankin
  • Cecília Salgado

Research Organisations

External Research Organisations

  • University of Groningen
  • Universidade Federal do Rio de Janeiro
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Details

Original languageEnglish
Pages (from-to)463-478
Number of pages16
JournalJournal of Number Theory
Volume236
Early online date30 Aug 2021
Publication statusPublished - Jul 2022

Abstract

We consider a family of smooth del Pezzo surfaces of degree four and study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

Keywords

    math.AG, math.NT, 14G05 (primary), 11G35, 11D09, 14D10 (secondary), Mordell-Weil group, Conic bundle, Brauer group, Elliptic fibration, Del Pezzo surface of degree 4

ASJC Scopus subject areas

Cite this

Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4. / Mitankin, Vladimir; Salgado, Cecília.
In: Journal of Number Theory, Vol. 236, 07.2022, p. 463-478.

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

Mitankin V, Salgado C. Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4. Journal of Number Theory. 2022 Jul;236:463-478. Epub 2021 Aug 30. doi: 10.48550/arXiv.2102.08798, 10.1016/j.jnt.2021.07.030
Mitankin, Vladimir ; Salgado, Cecília. / Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4. In: Journal of Number Theory. 2022 ; Vol. 236. pp. 463-478.
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N1 - Funding Information: Acknowledgments. We would like to thank Martin Bright, Yuri Manin and Bianca Viray for useful discussions. We are grateful to Leibniz University Hannover, the Max Planck Institute for Mathematics in Bonn and the Federal University of Rio de Janeiro for their hospitality while working on this article. Vladimir Mitankin was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft . Cecília Salgado was partially supported by FAPERJ grant E-26/202.786/2019 , CNPq grant PQ2 310070/2017-1 and the Capes-Humboldt program.

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