Definition 37.7.2. Let $h : Z \to X$ be a formally unramified morphism of schemes.

The

*universal first order thickening*of $Z$ over $X$ is the thickening $Z \subset Z'$ constructed in Lemma 37.7.1.The

*conormal sheaf of $Z$ over $X$*is the conormal sheaf of $Z$ in its universal first order thickening $Z'$ over $X$.

We often denote the conormal sheaf $\mathcal{C}_{Z/X}$ in this situation.

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