Lemma 29.32.9. Let $f : X \to Y$, $g : Y \to S$ be morphisms of schemes. Then there is a canonical exact sequence

where the maps come from applications of Lemma 29.32.8.

Lemma 29.32.9. Let $f : X \to Y$, $g : Y \to S$ be morphisms of schemes. Then there is a canonical exact sequence

\[ f^*\Omega _{Y/S} \to \Omega _{X/S} \to \Omega _{X/Y} \to 0 \]

where the maps come from applications of Lemma 29.32.8.

**Proof.**
This is the sheafified version of Algebra, Lemma 10.131.7. Alternatively, there is a general version for morphisms of ringed spaces, see Modules, Lemma 17.28.14.
$\square$

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## Comments (2)

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