Definition 71.2.2. Let S be a scheme. Let X be an algebraic space over S. Let \mathcal{F} be a quasi-coherent sheaf on X. Let x \in |X|.
We say x is weakly associated to \mathcal{F} if the equivalent conditions (1), (2), and (3) of Lemma 71.2.1 are satisfied.
We denote \text{WeakAss}(\mathcal{F}) the set of weakly associated points of \mathcal{F}.
The weakly associated points of X are the weakly associated points of \mathcal{O}_ X.
If X is locally Noetherian we will say x is associated to \mathcal{F} if and only if x is weakly associated to \mathcal{F} and we set \text{Ass}(\mathcal{F}) = \text{WeakAss}(\mathcal{F}). Finally (still assuming X is locally Noetherian), we will say x is an associated point of X if and only if x is a weakly associated point of X.
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