Lemma 17.17.5. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $U \subset X$ be open. The sheaf $j_{U!}\mathcal{O}_ U$ is a flat sheaf of $\mathcal{O}_ X$-modules.

Proof. The stalks of $j_{U!}\mathcal{O}_ U$ are either zero or equal to $\mathcal{O}_{X, x}$. Apply Lemma 17.17.2. $\square$

Comment #780 by Anfang Zhou on

Typos in the proof.

1.$j_{U!}\mathcal{O}_U$.

2."either zero or equal"

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