Lemma 31.11.6 (0AXV)—The Stacks project

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Lemma 31.11.6. Let $f : X \to Y$ be a flat morphism of integral schemes. Let $\mathcal{G}$ be a torsion free quasi-coherent $\mathcal{O}_ Y$ -module. Then $f^*\mathcal{G}$ is a torsion free $\mathcal{O}_ X$ -module.

Proof. Omitted. See More on Algebra, Lemma 15.22.4 for the algebraic analogue. $\square$

Comments (2)

Comment #8390 by timothy de deyn on May 10, 2023 at 09:35

this should link to https://stacks.math.columbia.edu/tag/0AXM

Comment #9000 by Stacks project on April 17, 2024 at 14:08

Thanks and fixed here.

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