Lemma 17.17.5 (05NH)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 17: Sheaves of Modules
Section 17.17: Flat modules
Lemma 17.17.5 (cite)

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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. $\square$

Comments (1)

Comment #780 by Anfang Zhou on July 01, 2014 at 22:18

Typos in the proof.

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

2."either zero or equal"

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