Lemma 76.31.2 (0D4N)—The Stacks project

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Lemma 76.31.2. Let $S$ be a scheme. Let $f : X \to Y$ be a finite type morphism of algebraic spaces over $S$ . Let

$n_{X/Y} : |Y| \to \{ -\infty , 0, 1, 2, 3, \ldots \}$

be the function which associates to $y \in |Y|$ the integer discussed in Lemma 76.31.1. If $g : Y' \to Y$ is a morphism then

$n_{X'/Y'} = n_{X/Y} \circ |g|$

where $X' \to Y'$ is the base change of $f$ .

Proof. This follows immediately from Lemma 76.31.1. $\square$

Comments (2)

Comment #8141 by Laurent Moret-Bailly on February 27, 2023 at 10:46

I think $\infty$ should be $-\infty$ .

Comment #8233 by Stacks Project on March 03, 2023 at 15:03

Thanks and fixed here.