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

1. $X$ is geometrically reduced,

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

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

Proof. Immediate from the definitions and Lemma 70.11.2. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).