The Stacks project

Lemma 37.60.14. Let $i : X \to Y$ be an immersion. If

  1. $i$ is perfect,

  2. $Y$ is locally Noetherian, and

  3. the conormal sheaf $\mathcal{C}_{X/Y}$ is finite locally free,

then $i$ is a regular immersion.

Proof. Translated into algebra, this is Divided Power Algebra, Proposition 23.11.3. $\square$

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