Definition 70.4.5. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. The relative weak assassin of $\mathcal{F}$ in $X$ over $Y$ is the set $\text{WeakAss}_{X/Y}(\mathcal{F}) \subset |X|$ consisting of those $x \in |X|$ such that the equivalent conditions of Lemma 70.4.4 are satisfied. If the fibres of $f$ are locally Noetherian (Definition 70.4.2) then we use the notation $\text{Ass}_{X/Y}(\mathcal{F})$.

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