Definition 29.54.1. Let $X$ be a scheme such that every quasi-compact open has finitely many irreducible components. We define the *normalization* of $X$ as the morphism

\[ \nu : X^\nu \longrightarrow X \]

which is the normalization of $X$ in the morphism $f : Y \to X$ (29.54.0.1) constructed above.

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