Lemma 59.106.3. Let $K$ be an object of $D^+((\mathit{Sch}/S)_{fppf})$. Then $K$ is in the essential image of $R\epsilon _* : D((\mathit{Sch}/S)_ h) \to D((\mathit{Sch}/S)_{fppf})$ if and only if $c^ K_{X, X', Z, E}$ is a quasi-isomorphism for every almost blow up square as in More on Flatness, Examples 38.37.10 and 38.37.11.

**Proof.**
We prove this by applying Cohomology on Sites, Lemma 21.29.2 whose hypotheses hold by Lemma 59.106.1 and More on Flatness, Lemma 38.37.12
$\square$

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