The Stacks project

Lemma 37.66.8. A separated locally quasi-finite morphism of schemes is ind-quasi-affine.

Proof. Let $f : X \to Y$ be a separated locally quasi-finite morphism of schemes. Let $V \subset Y$ be affine and $U \subset f^{-1}(V)$ quasi-compact open. We have to show $U$ is quasi-affine. Since $U \to V$ is a separated quasi-finite morphism of schemes, this follows from Zariski's Main Theorem. See Lemma 37.43.2. $\square$

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