Proposition 59.106.2. 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 (59.106.0.1) in $(\mathit{Sch}/S)_ h$ with $X$ affine.

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, Proposition 38.37.9. $\square$

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