The Stacks project

Definition 70.14.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{I} \subset \mathcal{O}_ X$ be a quasi-coherent sheaf of ideals of finite type. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. The subsheaf $\mathcal{F}' \subset \mathcal{F}$ defined in Lemma 70.14.2 above is called the subsheaf of sections annihilated by $\mathcal{I}$.