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arXiv · 2608.28204

Arithmetic purity of strong approximation for toric varieties with constant global sections

Dasheng Wei·Fei Xu·Yi Zhu
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Abstract

Let $X$ be a smooth toric variety over a number field $k$ such that the global sections of $X$ are constant. We show that $U(k)$ is dense in $U(\mathbf A_k)^{\text{Br}_1 (U)}$ for any open subset $U$ of $X$ such that the codimension of $X\setminus U$ in $X$ is at least 2.

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Dasheng Wei, Fei Xu, Yi Zhu. 2026-08-28. Arithmetic purity of strong approximation for toric varieties with constant global sections. https://arxiv.org/abs/2608.28204

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