Lemma 68.11.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Consider the map
This map is always injective. If $X$ is decent then this map is a bijection.
Lemma 68.11.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Consider the map
This map is always injective. If $X$ is decent then this map is a bijection.
Proof. We have seen in Properties of Spaces, Lemma 66.4.12 that the map is an injection in general. By Lemma 68.5.1 it is surjective when $X$ is decent (actually one can say this is part of the definition of being decent). $\square$
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