Lemma 77.12.2. In Situation 77.12.1 consider

\[ K = R\mathop{\mathrm{lim}}\nolimits _{D_\mathit{QCoh}(\mathcal{O}_ X)}(\mathcal{F}_ n) = DQ_ X(R\mathop{\mathrm{lim}}\nolimits _{D(\mathcal{O}_ X)}\mathcal{F}_ n) \]

Then $K$ is in $D^ b_{\mathit{QCoh}}(\mathcal{O}_ X)$ and in fact $K$ has nonzero cohomology sheaves only in degrees $\geq 0$.

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