[IV Theorem 13.1.3, EGA]

Lemma 29.28.4. Let $f : X \to S$ be a morphism of schemes. Let $n \geq 0$. Assume $f$ is locally of finite type. The set

$U_ n = \{ x \in X \mid \dim _ x X_{f(x)} \leq n\}$

is open in $X$.

Proof. This is immediate from Algebra, Lemma 10.125.6 $\square$

Comment #2695 by on

A reference is EGA IV_3, Theorem 13.1.3

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