Lemma 15.23.16. Let $R$ be a Noetherian domain. Let $M$ be a finite reflexive $R$-module. Let $\mathfrak p \subset R$ be a prime ideal.

If $\text{depth}(R_\mathfrak p) \geq 2$, then $\text{depth}(M_\mathfrak p) \geq 2$.

If $R$ is $(S_2)$, then $M$ is $(S_2)$.

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