The Stacks project

Definition 26.17.7. Let $f : X \to Y$ be a morphism of schemes. Let $Z \subset Y$ be a closed subscheme of $Y$. The inverse image $f^{-1}(Z)$ of the closed subscheme $Z$ is the closed subscheme $Z \times _ Y X$ of $X$. See Lemma 26.17.6 above.

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