The Stacks project

Lemma 29.54.10. Let $X$ be an integral, Japanese scheme. The normalization $\nu : X^\nu \to X$ is a finite morphism.

Proof. Follows from the definition (Properties, Definition 28.13.1) and Lemma 29.54.3. Namely, in this case the lemma says that $\nu ^{-1}(\mathop{\mathrm{Spec}}(A))$ is the spectrum of the integral closure of $A$ in its field of fractions. $\square$

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