The Stacks project

Definition 76.15.5. Let $S$ be a scheme. Let $h : Z \to X$ be a formally unramified morphism of algebraic spaces over $S$.

  1. The universal first order thickening of $Z$ over $X$ is the thickening $Z \subset Z'$ constructed in Lemma 76.15.4.

  2. 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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