Let $X$ be a smooth proper variety over $\mathbb{Q}$ with good ordinary reduction $X_0$ at a prime $p$.
Can $X_0$ and $X$ have different (geometric) picard numbers?
Let $X$ be a smooth proper variety over $\mathbb{Q}$ with good ordinary reduction $X_0$ at a prime $p$.
Can $X_0$ and $X$ have different (geometric) picard numbers?
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