Lemma 29.17.8. 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 27.27.1 this follows from Lemma 29.17.7.
$\square$

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