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November 11, 2016November 11, 2016 nachodarago

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 $\mathbb{Q}$ .

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