Let $X,X'$ be normal, proper and flat $\mathbb{Z}$-schemes. Write $X_{\mathbb{Q}}$ for the generic fiber of $X$, i.e. $X_{\mathbb{Q}}:=X \times_{Spec (\mathbb{Z})} Spec (\mathbb{Q})$.
Let us assume that there is an isomorphism $X_{\mathbb{Q}}\cong X'_{\mathbb{Q}}$ of $\mathbb{Q}$-schemes. The following fact seems to be well known:
There exists a finite set of prime numbers $\Sigma=\{p_1,...,p_{n}\} \subset \mathbb{Z}$ such that the above (generic) isomorphism extends to an isomorphism of $\mathbb{Z}(\Sigma^{-1})$-schemes (where $\mathbb{Z}(\Sigma^{-1}):=\mathbb{Z}[p_{1}^{-1},...,p_{n}^{-1}]$), i.e. we have
$X \times_{Spec(\mathbb{Z})} Spec(\mathbb{Z}(\Sigma^{-1})) \cong X' \times_{Spec(\mathbb{Z})}Spec(\mathbb{Z}(\Sigma^{-1}))$
Can anyone give me a reference for this statement or, if it seems reasonable, even a (sketch of a) proof?