Lemma 32.18.3 (0H3V)—The Stacks project

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Part 2: Schemes
Chapter 32: Limits of Schemes
Section 32.18: Limits and dimensions of fibres
Lemma 32.18.3 (cite)

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Lemma 32.18.3. Assumptions and notation as in Situation 32.8.1. Let $d \geq 0$. If

$f$ has relative dimension $\leq d$ (Morphisms, Definition 29.29.1), and
$f_0$ is locally of finite type,

then there exists an $i$ such that $f_ i$ has relative dimension $\leq d$.

Proof. Follows immediately from Lemma 32.18.1. $\square$

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