The Stacks project

Lemma 37.64.8. Let $f : X \to Y$ be a weakly étale morphism of schemes. Then $f$ is formally unramified, i.e., $\Omega _{X/Y} = 0$.

Proof. Recall that $f$ is formally unramified if and only if $\Omega _{X/Y} = 0$ by Lemma 37.6.7. Via Lemma 37.64.4 and Morphisms, Lemma 29.32.5 this follows from the case of rings which is More on Algebra, Lemma 15.104.12. $\square$

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