Lemma 70.11.3. Let $k$ be a field. Let $X$ be an algebraic space over $k$. The following are equivalent

$X$ is geometrically reduced,

for some surjective étale morphism $U \to X$ where $U$ is a scheme, $U$ is geometrically reduced,

for any étale morphism $U \to X$ where $U$ is a scheme, $U$ is geometrically reduced.

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