Lemma 30.17.8 (0EBE)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 30: Cohomology of Schemes
Section 30.17: Ample invertible sheaves and cohomology
Lemma 30.17.8 (cite)

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Lemma 30.17.8. Let $X$ be a quasi-affine scheme. If $H^ p(X, \mathcal{O}_ X) = 0$ for $p > 0$ , then $X$ is affine.

Proof. Since $\mathcal{O}_ X$ is ample by Properties, Lemma 28.27.1 this follows from Lemma 30.17.7. $\square$

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