Lemma 37.30.6 (0D4J)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.30: Dimension of fibres
Lemma 37.30.6 (cite)

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Lemma 37.30.6. Let $f : X \to Y$ be a proper, flat morphism of schemes of finite presentation. Let $n_{X/Y}$ be the function on $Y$ giving the dimension of fibres of $f$ introduced in Lemma 37.30.2. Then $n_{X/Y}$ is locally constant.

Proof. Immediate consequence of Lemmas 37.30.4 and 37.30.5. $\square$

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