Lemma 37.13.8. Let $i : Z \to X$ be an immersion of schemes. Then $\mathop{N\! L}\nolimits _{Z/X}$ is isomorphic to $\mathcal{C}_{Z/X}[1]$ in $D(\mathcal{O}_ Z)$ where $\mathcal{C}_{Z/X}$ is the conormal sheaf of $Z$ in $X$.

**Proof.**
This follows from Algebra, Lemma 10.133.6, Morphisms, Lemma 29.31.2, and Lemma 37.13.2.
$\square$

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