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

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.

12 pages