Lemma 31.12.4. Let $X$ be an integral locally Noetherian scheme. Let $\mathcal{F}$ be a coherent $\mathcal{O}_ X$-module.

If $\mathcal{F}$ is reflexive, then $\mathcal{F}$ is torsion free.

The map $j : \mathcal{F} \longrightarrow \mathcal{F}^{**}$ is injective if and only if $\mathcal{F}$ is torsion free.

## Comments (2)

Comment #6273 by Matthieu Romagny on

Comment #6395 by Johan on