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PreprintCC BY 4.0arXiv

Brauer groups of generalised Markoff surfaces

  • Zheshuai Tian
  • Dasheng Wei
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Abstract

Let k be a field of characteristic zero with a,b,c∈ k× and let m∈ k∖{0,4abc}. We compute the Brauer group of the generalised Markoff surface ax2+by2+cz2−xyz=m. We also construct several counterexamples to the integral Hasse principle, which are explained by the Brauer--Manin obstruction.

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Cite

BibTeXRIS
BibTeX
@misc{tian2026brauer,
  title = {{Brauer groups of generalised Markoff surfaces}},
  author = {Zheshuai Tian and Dasheng Wei},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07454},
  eprint = {2611.07454},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07454},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Brauer groups of generalised Markoff surfaces
AU  - Zheshuai Tian
AU  - Dasheng Wei
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07454
UR  - https://arxiv.org/abs/2611.07454
AB  - Let k be a field of characteristic zero with a,b,c∈ k^× and let m∈ k∖{0,4abc}. We compute the Brauer group of the generalised Markoff surface ax^2+by^2+cz^2−xyz=m. We also construct several counterexamples to the integral Hasse principle, which are explained by the Brauer--Manin obstruction.
ER  -