# Local to Global

Let $R$ be an integral domain of finite type over $\mathbb{Z}$, whose quotient field is of characteristic zero. Let $\alpha\in R$ be an element such that at every closed point $\mathfrak{p}$ the image of $\alpha$ in the residue field $R/\mathfrak{p}$ lies in the prime field $\mathbb{F}_p$ (where $p = \mathfrak{p}\cap\mathbb{Z})$. Prove that $\alpha$ must be in $\mathbb{Q}$.