Lemma 15.23.14 (0AV9)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.23: Reflexive modules
Lemma 15.23.14 (cite)

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Lemma 15.23.14. Let $R$ be a Noetherian domain. Let $\varphi : M \to N$ be a map of $R$ -modules. Assume $M$ is finite, $N$ is torsion free, and that for every prime $\mathfrak p$ of $R$ one of the following happens

$M_\mathfrak p \to N_\mathfrak p$ is an isomorphism, or
$\text{depth}(M_\mathfrak p) \geq 2$ .

Then $\varphi$ is an isomorphism.

Proof. This is a special case of Lemma 15.23.13. $\square$

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