The Stacks project

Lemma 54.16.11. Let $S$ be a Noetherian scheme. Let $f : X \to S$ be a proper morphism with $X$ regular of dimension $2$. Then $X$ is projective over $S$.

Proof. This follows from Lemma 54.16.10 and Morphisms, Lemma 29.43.13. $\square$

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