The Stacks project

Definition 31.7.1. Let $f : X \to S$ be a morphism of schemes. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. The relative assassin of $\mathcal{F}$ in $X$ over $S$ is the set

where $\mathcal{F}_ s = (X_ s \to X)^*\mathcal{F}$ is the restriction of $\mathcal{F}$ to the fibre of $f$ at $s$.