Lemma 18.28.7. Let $\mathcal{C}$ be a category. Let $\mathcal{O}$ be a presheaf of rings. Let $U$ be an object of $\mathcal{C}$. Consider the functor $j_ U : \mathcal{C}/U \to \mathcal{C}$.

The presheaf of $\mathcal{O}$-modules $j_{U!}\mathcal{O}_ U$ (see Remark 18.19.7) is flat.

If $\mathcal{C}$ is a site, $\mathcal{O}$ is a sheaf of rings, $j_{U!}\mathcal{O}_ U$ is a flat sheaf of $\mathcal{O}$-modules.

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