Lemma 20.12.5. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of ringed spaces. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_ X$-modules. If $\mathcal{F}$ is flasque, then $R^ pf_*\mathcal{F} = 0$ for $p > 0$.

Proof. Immediate from Lemma 20.7.3 and Lemma 20.12.3. $\square$

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