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arXiv · 2604.10498

Remarks on Brauer-Manin obstruction for Weil restrictions

Sheng Chen·Kai Huang
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Abstract

Given a finite extension $K/k$ of number fields and a smooth quasi-projective variety $X$ over $K$. If the abelianized fundamental group of $X$ is trivial, we prove that there is a natural identification between Brauer-Manin sets of $X$ and its Weil restriction $R_{K/k}X$. If $X$ is projective and $Pic(X\times_{K}\overline{k})$ is a torsion-free abelian group, we prove that there is a natural identification between algebraic Brauer-Manin sets of $X$ and $R_{K/k}X$.

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Sheng Chen, Kai Huang. 2026-04-12. Remarks on Brauer-Manin obstruction for Weil restrictions. https://arxiv.org/abs/2604.10498

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