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The Stacks project

Lemma 76.44.6. Let $S$ be a scheme. Let $i : Z \to X$ be an immersion of algebraic spaces over $S$. Then $i$ is a quasi-regular immersion if and only if the following conditions are satisfied

  1. $i$ is locally of finite presentation,

  2. the conormal sheaf $\mathcal{C}_{Z/X}$ is finite locally free, and

  3. the map (76.6.1.2) is an isomorphism.

Proof. Follows from the case of schemes (Divisors, Lemma 31.21.5) via étale localization (use Definition 76.44.2 and Lemma 76.6.2). $\square$

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