Brauer groups of generalised Markoff surfaces

Zheshuai Tian; Dasheng Wei

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arXiv · 2611.07454

Brauer groups of generalised Markoff surfaces

Zheshuai Tian·Dasheng Wei

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Abstract

Let $k$ be a field of characteristic zero with $a,b,c\in k^\times$ and let $m\in k\setminus\{0,4abc\}$. 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.

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BibTeX RIS

Zheshuai Tian, Dasheng Wei. 2026-11-05. Brauer groups of generalised Markoff surfaces. https://arxiv.org/abs/2611.07454

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