The Stacks project

Lemma 38.13.5. Let $f : X \to S$ be a morphism which is locally of finite type. Let $\mathcal{F}$ be a finite type quasi-coherent sheaf on $X$ which is flat over $S$. Let $\mathcal{G}$ be a quasi-coherent sheaf on $S$. Then we have

\[ \text{WeakAss}_ X(\mathcal{F} \otimes _{\mathcal{O}_ X} f^*\mathcal{G}) = \bigcup \nolimits _{s \in \text{WeakAss}_ S(\mathcal{G})} \text{Ass}_{X_ s}(\mathcal{F}_ s) \]

Proof. Immediate consequence of Lemma 38.13.3. $\square$

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