Lemma 37.7.3. Let $i : Z \to X$ be an immersion of schemes. Then

$i$ is formally unramified,

the universal first order thickening of $Z$ over $X$ is the first order infinitesimal neighbourhood of $Z$ in $X$ of Definition 37.5.1, and

the conormal sheaf of $i$ in the sense of Morphisms, Definition 29.31.1 agrees with the conormal sheaf of $i$ in the sense of Definition 37.7.2.

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