Lemma 29.53.6 (035K)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.53: Relative normalization
Lemma 29.53.6 (cite)

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Lemma 29.53.6. Let $f : Y \to X$ be a quasi-compact and quasi-separated morphism of schemes. Let $U \subset X$ be an open subscheme and set $V = f^{-1}(U)$ . Then the normalization of $U$ in $V$ is the inverse image of $U$ in the normalization of $X$ in $Y$ .

Proof. Clear from the construction. $\square$

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