Lemma 71.2.11. Let S be a scheme. Let X be an algebraic space over S. Let \varphi : \mathcal{F} \to \mathcal{G} be a map of quasi-coherent \mathcal{O}_ X-modules. Assume that for every x \in |X| at least one of the following happens
\mathcal{F}_{\overline{x}} \to \mathcal{G}_{\overline{x}} is injective, or
x \not\in \text{WeakAss}(\mathcal{F}).
Then \varphi is injective.
Comments (0)