Lemma 71.3.1. Let S be a scheme. Let f : X \to Y be an affine morphism of algebraic spaces over S. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Then we have
\text{WeakAss}_ S(f_*\mathcal{F}) \subset f(\text{WeakAss}_ X(\mathcal{F}))
Proof. Choose a scheme V and a surjective étale morphism V \to Y. Set U = X \times _ Y V. Then U \to V is an affine morphism of schemes. By our definition of weakly associated points the problem is reduced to the morphism of schemes U \to V. This case is treated in Divisors, Lemma 31.6.1. \square
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