The Stacks project

Remark 48.30.5. Let $j : U \to X$ be an open immersion of Noetherian schemes. Sending $K \in D^ b_{\textit{Coh}}(\mathcal{O}_ U)$ to a Deligne system whose restriction to $U$ is $K$ determines a functor

\[ Rj_! : D^ b_{\textit{Coh}}(\mathcal{O}_ U) \longrightarrow \text{Pro-}D^ b_{\textit{Coh}}(\mathcal{O}_ X) \]

which is “exact” by Lemma 48.30.4 and which is “left adjoint” to the functor $j^* : D^ b_{\textit{Coh}}(\mathcal{O}_ X) \to D^ b_{\textit{Coh}}(\mathcal{O}_ U)$ by Lemma 48.30.1.

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