The Stacks project

Definition 82.4.2. Let $S$ be a scheme and let $X$ be an algebraic space over $S$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Let $x \in |X|$. Let $d \in \{ 0, 1, 2, \ldots , \infty \}$. We say $\mathcal{F}$ has length $d$ at $x$ if the equivalent conditions of Lemma 82.4.1 are satisfied.