Lemma 73.8.3. Let S be a scheme. Let f : Y \to X be a surjective proper morphism of algebraic spaces over S. Then \{ Y \to X\} is a ph covering.
Proof. Let U \to X be a morphism with U affine. By Chow's lemma (in the weak form given as Cohomology of Spaces, Lemma 69.18.1) we see that there is a surjective proper morphism of schemes V \to U which factors through Y \times _ X U \to U. Taking any finite affine open cover of V we obtain a standard ph covering of U refining \{ X \times _ Y U \to U\} as desired. \square
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