The Stacks project

Lemma 84.7.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. For $\mathcal{F}$ a quasi-coherent $\mathcal{O}_ X$-module the maps

\[ \pi _ X^*\mathcal{F} \longrightarrow R\epsilon _{X, *}(a_ X^*\mathcal{F}) \quad \text{and}\quad \mathcal{F} \longrightarrow Ra_{X, *}(a_ X^*\mathcal{F}) \]

are isomorphisms.

Proof. This is an immediate consequence of parts (6) and (7) of Lemma 84.7.1. $\square$

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