Lemma 37.13.9 (0FV2)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.13: The naive cotangent complex
Lemma 37.13.9 (cite)

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Lemma 37.13.9. 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 10.134.6, Morphisms, Lemma 29.31.2, and Lemma 37.13.2. $\square$

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