Fields of Definition of Rational Points on Varieties

Details Fields of Definition of Rational Points on Varieties Fields of Definition of Rational Points on Varieties

2005-05-17

arxiv.org/abs/math/0505364v1

Mathematics

Number Theory

6 pages

Scientific paper

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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