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

Dasheng Wei, Fei Xu, Yi Zhu

Source record

Source: arXiv

Published: Aug 28, 2026

arXiv: 2608.28204

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Source 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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Arithmetic purity of strong approximation for toric varieties with constant global sections — Mathematical Frontier Network