The Stacks project

Lemma 37.64.10. Let $f : X \to Y$ be a morphism of schemes. If $Y$ is reduced and $f$ weakly étale, then $X$ is reduced.

Proof. Via Lemma 37.64.4 this follows from the case of rings which is More on Algebra, Lemma 15.104.8. $\square$

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