The Stacks project

Lemma 75.48.12. 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 37.60.22, by ├ętale localization, see Lemma 75.15.11. (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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