Definition 26.18.3. Properties and base change.

1. Let $\mathcal{P}$ be a property of schemes over a base. We say that $\mathcal{P}$ is preserved under arbitrary base change, or simply that $\mathcal{P}$ is preserved under base change if whenever $X/S$ has $\mathcal{P}$, any base change $X_{S'}/S'$ has $\mathcal{P}$.

2. Let $\mathcal{P}$ be a property of morphisms of schemes over a base. We say that $\mathcal{P}$ is preserved under arbitrary base change, or simply that preserved under base change if whenever $f : X \to Y$ over $S$ has $\mathcal{P}$, any base change $f' : X_{S'} \to Y_{S'}$ over $S'$ has $\mathcal{P}$.

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