Lemma 76.31.5 (0D4R)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.31: Dimension of fibres
Lemma 76.31.5 (cite)

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Lemma 76.31.5. Let $S$ be a scheme. Let $f : X \to Y$ be a proper, flat, finitely presented morphism of algebraic spaces over $S$ . Let $n_{X/Y}$ be the function on $Y$ giving the dimension of fibres of $f$ introduced in Lemma 76.31.2. Then $n_{X/Y}$ is locally constant.

Proof. Immediate consequence of Lemmas 76.31.3 and 76.31.4. $\square$

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