Lemma 28.22.5. Let $X$ be a quasi-compact and quasi-separated scheme. Let $U \subset X$ be a quasi-compact open. Let $\mathcal{G}$ be an $\mathcal{O}_ U$-module.

If $\mathcal{G}$ is quasi-coherent and of finite type, then there exists a quasi-coherent $\mathcal{O}_ X$-module $\mathcal{G}'$ of finite type such that $\mathcal{G}'|_ U = \mathcal{G}$.

If $\mathcal{G}$ is of finite presentation, then there exists an $\mathcal{O}_ X$-module $\mathcal{G}'$ of finite presentation such that $\mathcal{G}'|_ U = \mathcal{G}$.

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