Lemma 21.52.6. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $U$ be an object of $\mathcal{C}$ which is quasi-compact and weakly contractible. Then $j_!\mathcal{O}_ U$ is a compact object of $D(\mathcal{O})$.
Lemma 21.52.6. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $U$ be an object of $\mathcal{C}$ which is quasi-compact and weakly contractible. Then $j_!\mathcal{O}_ U$ is a compact object of $D(\mathcal{O})$.
Proof. Combine Lemmas 21.52.5 and 21.51.1 with Modules on Sites, Lemma 18.30.3. $\square$
Comments (0)