Lemma 37.11.11. Let f : X \to Y, g : Y \to S be morphisms of schemes. Assume f is formally smooth. Then
0 \to f^*\Omega _{Y/S} \to \Omega _{X/S} \to \Omega _{X/Y} \to 0
(see Morphisms, Lemma 29.32.9) is short exact.
Proof. The algebraic version of this lemma is the following: Given ring maps A \to B \to C with B \to C formally smooth, then the sequence
0 \to C \otimes _ B \Omega _{B/A} \to \Omega _{C/A} \to \Omega _{C/B} \to 0
of Algebra, Lemma 10.131.7 is exact. This is Algebra, Lemma 10.138.9. \square
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