Lemma 76.12.2. In Situation 76.12.1 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 $\geq 0$.

## Comments (0)