Definition 70.11.1. Let $k$ be a field. Let $X$ be an algebraic space over $k$.

Let $x \in |X|$ be a point. We say $X$ is

*geometrically reduced at $x$*if $\mathcal{O}_{X, \overline{x}}$ is geometrically reduced over $k$.We say $X$ is

*geometrically reduced*over $k$ if $X$ is geometrically reduced at every point of $X$.

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