Fields of Definition of Rational Points on Varieties

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 $M_X=K$

6 pages