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Cubic surfaces failing the integral Hasse principle

Research output: Working paper/Preprint › Preprint

Authors

  • Julian Lyczak
  • Vladimir Mitankin
  • H. Uppal

Research Organisations

Details

Original languageEnglish
Number of pages38
Publication statusE-pub ahead of print - 16 Nov 2023

Abstract

We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such counterexamples are distributed across the family of affine diagonal cubic surfaces and how often such surfaces satisfy integral strong approximation off $\infty$.

Keywords

    math.NT, math.AG, 14G12 (primary), 11D25, 14G05, 14F22 (secondary)

Cite this

Cubic surfaces failing the integral Hasse principle. / Lyczak, Julian; Mitankin, Vladimir; Uppal, H.
2023.

Research output: Working paper/Preprint › Preprint

Lyczak, J., Mitankin, V., & Uppal, H. (2023). Cubic surfaces failing the integral Hasse principle. Advance online publication. https://doi.org/10.48550/arXiv.2311.10008
Lyczak J, Mitankin V, Uppal H. Cubic surfaces failing the integral Hasse principle. 2023 Nov 16. Epub 2023 Nov 16. doi: 10.48550/arXiv.2311.10008
Lyczak, Julian ; Mitankin, Vladimir ; Uppal, H. / Cubic surfaces failing the integral Hasse principle. 2023.
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