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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.

Comments (2)

Comment #302 by UT on

I think it should be instead of in the definition.

There are also:

  • 6 comment(s) on Section 10.47: Geometrically irreducible algebras

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View Definition 10.47.4 as pdf