Lemma 29.32.14 (01UY)—The Stacks project

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Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.32: Sheaf of differentials of a morphism
Lemma 29.32.14 (cite)

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Lemma 29.32.14. If $X \to S$ is an immersion, or more generally a monomorphism, then $\Omega _{X/S}$ is zero.

Proof. This is true because $\Delta _{X/S}$ is an isomorphism in this case and hence has trivial conormal sheaf. Hence $\Omega _{X/S} = 0$ by Lemma 29.32.7. The algebraic version is Algebra, Lemma 10.131.4. $\square$

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