Lemma 36.6.2. Let $X$ be a scheme. Let $T \subset X$ be a closed subset such that $X \setminus T$ is a retrocompact open of $X$. Let $i : T \to X$ be the inclusion.

For $E$ in $D_\mathit{QCoh}(\mathcal{O}_ X)$ we have $i_*R\mathcal{H}_ T(E)$ in $D_{\mathit{QCoh}, T}(\mathcal{O}_ X)$.

The functor $i_* \circ R\mathcal{H}_ T : D_\mathit{QCoh}(\mathcal{O}_ X) \to D_{\mathit{QCoh}, T}(\mathcal{O}_ X)$ is right adjoint to the inclusion functor $D_{\mathit{QCoh}, T}(\mathcal{O}_ X) \to D_\mathit{QCoh}(\mathcal{O}_ X)$.

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