Lemma 76.44.8 (09S0)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.44: Regular immersions
Lemma 76.44.8 (cite)

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Lemma 76.44.8. Let $S$ be a scheme. Let $i : Z \to Y$ and $j : Y \to X$ be immersions of algebraic spaces over $S$ .

If $i$ and $j$ are Koszul-regular immersions, so is $j \circ i$ .
If $i$ and $j$ are $H_1$ -regular immersions, so is $j \circ i$ .
If $i$ is an $H_1$ -regular immersion and $j$ is a quasi-regular immersion, then $j \circ i$ is a quasi-regular immersion.

Proof. Immediate from the case of schemes, see Divisors, Lemma 31.21.7. $\square$

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