Lemma 69.8.2. Let $S$ be a scheme. Let $f : X \to Y$ be an affine morphism of algebraic spaces over $S$. Then $R^ if_*\mathcal{F} = 0$ for $i > 0$ and any quasi-coherent $\mathcal{O}_ X$-module $\mathcal{F}$.

**Proof.**
Recall that an affine morphism of algebraic spaces is representable. Hence this follows from (69.3.0.1) and Cohomology of Schemes, Lemma 30.2.3.
$\square$

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