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
\[ \text{Ass}_{X/S}(\mathcal{F}) = \bigcup \nolimits _{s \in S} \text{Ass}_{X_ s}(\mathcal{F}_ s) \]
where $\mathcal{F}_ s = (X_ s \to X)^*\mathcal{F}$ is the restriction of $\mathcal{F}$ to the fibre of $f$ at $s$.
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