Definition 10.43.1. Let $k$ be a field. Let $S$ be a $k$-algebra. We say $S$ is geometrically reduced over $k$ if for every field extension $K/k$ the $K$-algebra $K \otimes _ k S$ is reduced.
Definition 10.43.1. Let $k$ be a field. Let $S$ be a $k$-algebra. We say $S$ is geometrically reduced over $k$ if for every field extension $K/k$ the $K$-algebra $K \otimes _ k S$ is reduced.
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