Lemma 15.23.4. Let $R$ be a Noetherian domain. Let $M$ be a finite $R$-module. The following are equivalent:

$M$ is reflexive,

$M_\mathfrak p$ is a reflexive $R_\mathfrak p$-module for all primes $\mathfrak p \subset R$, and

$M_\mathfrak m$ is a reflexive $R_\mathfrak m$-module for all maximal ideals $\mathfrak m$ of $R$.

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