Proposition 73.11.5. Let $S$ be a scheme. Let $X$ be a quasi-compact algebraic space over $S$ with affine diagonal. Then the functor (73.5.1.1)
is an equivalence with quasi-inverse given by $RQ_ X$.
Proposition 73.11.5. Let $S$ be a scheme. Let $X$ be a quasi-compact algebraic space over $S$ with affine diagonal. Then the functor (73.5.1.1)
is an equivalence with quasi-inverse given by $RQ_ X$.
Proof. Let $V \to W$ be an étale morphism with $V$ affine and $W$ a quasi-compact open subspace of $X$. Then the morphism $V \to W$ is affine as $V$ is affine and $W$ has affine diagonal (Morphisms of Spaces, Lemma 65.20.11). Lemma 73.11.1 then guarantees that the assumption of Lemma 73.11.4 holds. Hence we conclude. $\square$
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Comment #450 by Pieter Belmans on
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