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Choose a prime $p$. Let $X$ be a smooth proper scheme over $\mathbb{Q}$. Does there exist a smooth proper scheme $X'$ over $\mathbb{Z}_{(p)}$ such that $X\otimes_{\mathbb{Q}} \mathbb{C}$ is diffeomorphic to $X'\otimes_{\mathbb{Z}_{(p)}}\mathbb{C}$?
Let $X$ be a smooth proper scheme over $\mathbb{Q}$. Does there exist a smooth proper scheme $X'$ over $\mathbb{Z}_{(p)}$ such that $X\otimes_{\mathbb{Q}} \mathbb{C}$ is diffeomorphic to $X'\otimes_{\mathbb{Z}_{(p)}}\mathbb{C}$?
Choose a prime $p$. Let $X$ be a smooth proper scheme over $\mathbb{Q}$. Does there exist a smooth proper scheme $X'$ over $\mathbb{Z}_{(p)}$ such that $X\otimes_{\mathbb{Q}} \mathbb{C}$ is diffeomorphic to $X'\otimes_{\mathbb{Z}_{(p)}}\mathbb{C}$?
The differential topology of varieties with good reduction
Let $X$ be a smooth proper scheme over $\mathbb{Q}$. Does there exist a smooth proper scheme $X'$ over $\mathbb{Z}_{(p)}$ such that $X\otimes_{\mathbb{Q}} \mathbb{C}$ is diffeomorphic to $X'\otimes_{\mathbb{Z}_{(p)}}\mathbb{C}$?
