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Let $X\subseteq \mathbb{C}^n$ be an irreducible variety defined over $\mathbb{Q}$. I would like to show that for all but finitely many prime $p$ the variety $X(\mathbb{F}_p)$, defined over $\mathbb{F}_p$, is geometrically reducibleirreducible, i.e., $X(\overline{\mathbb{F}}_p)$ is irreducible. Can someone give me a hint or a reference?

Thanks

Let $X\subseteq \mathbb{C}^n$ be an irreducible variety defined over $\mathbb{Q}$. I would like to show that for all but finitely many prime $p$ the variety $X(\mathbb{F}_p)$, defined over $\mathbb{F}_p$, is geometrically reducible, i.e., $X(\overline{\mathbb{F}}_p)$ is irreducible. Can someone give me a hint or a reference?

Thanks

Let $X\subseteq \mathbb{C}^n$ be an irreducible variety defined over $\mathbb{Q}$. I would like to show that for all but finitely many prime $p$ the variety $X(\mathbb{F}_p)$, defined over $\mathbb{F}_p$, is geometrically irreducible, i.e., $X(\overline{\mathbb{F}}_p)$ is irreducible. Can someone give me a hint or a reference?

Thanks

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M.B
  • 2.5k
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  • 31

Geometrically irreducible variety

Let $X\subseteq \mathbb{C}^n$ be an irreducible variety defined over $\mathbb{Q}$. I would like to show that for all but finitely many prime $p$ the variety $X(\mathbb{F}_p)$, defined over $\mathbb{F}_p$, is geometrically reducible, i.e., $X(\overline{\mathbb{F}}_p)$ is irreducible. Can someone give me a hint or a reference?

Thanks