The Stacks project

Regular immersions are stable under flat base change.

Lemma 76.44.5. Let $S$ be a scheme. Let $i : Z \to X$ be a Koszul-regular, $H_1$-regular, or quasi-regular immersion of algebraic spaces over $S$. Let $X' \to X$ be a flat morphism of algebraic spaces over $S$. Then the base change $i' : Z \times _ X X' \to X'$ is a Koszul-regular, $H_1$-regular, or quasi-regular immersion.

Proof. Via Definition 76.44.2 (and the definition of a flat morphism of algebraic spaces in Morphisms of Spaces, Section 67.30) this lemma reduces to the case of schemes, see Divisors, Lemma 31.21.4. $\square$

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