Lemma 76.48.12. Let $S$ be a scheme. Let $f : X \to Y$ be a local complete intersection morphism of algebraic spaces over $S$. Then $f$ is unramified if and only if $f$ is formally unramified and in this case the conormal sheaf $\mathcal{C}_{X/Y}$ is finite locally free on $X$.
Proof. This follows from the corresponding result for morphisms of schemes, see More on Morphisms, Lemma 37.62.22, by étale localization, see Lemma 76.15.11. (Note that in the situation of this lemma the morphism $V \to U$ is unramified and a local complete intersection morphism by definition.) $\square$
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