Definition 10.47.4. Let $k$ be a field. Let $S$ be a $k$-algebra. We say $S$ is geometrically irreducible over $k$ if for every field extension $k'/k$ the spectrum of $S \otimes _ k k'$ is irreducible1.
[1] An irreducible space is nonempty.
Definition 10.47.4. Let $k$ be a field. Let $S$ be a $k$-algebra. We say $S$ is geometrically irreducible over $k$ if for every field extension $k'/k$ the spectrum of $S \otimes _ k k'$ is irreducible1.
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