Definition 31.22.2. Let $f : X \to S$ be a morphism of schemes. Let $i : Z \to X$ be an immersion.

1. We say $i$ is a relative quasi-regular immersion if $Z \to S$ is flat and $i$ is a quasi-regular immersion.

2. We say $i$ is a relative $H_1$-regular immersion if $Z \to S$ is flat and $i$ is an $H_1$-regular immersion.

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