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Fields of Definition of Rational Points on Varieties

Jordan Rizov
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Abstract

Let $X$ be a scheme over a field $K$ and let $M_X$ be the intersection of all subfields $L$ of $\bar K$ such that $X$ has a $L$-valued point. In this note we prove that for a variety $X$ over a field $K$ finitely generated over its prime field one has that $M_X = K$

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Jordan Rizov. 2005-05-17. Fields of Definition of Rational Points on Varieties. https://arxiv.org/abs/math/0505364

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