Some Applications of the Hales-Jewett Theorem to Field Arithmetic

Details Some Applications of the Hales-Jewett Theorem to Field Arithmetic Some Applications of the Hales-Jewett Theorem to Field Arithmetic

2012-02-06

arxiv.org/abs/1202.1185v1

Mathematics

Number Theory

10 pages

Scientific paper

Let $K$ be a field whose absolute Galois group is finitely generated. If $K$ neither finite nor of characteristic 2, then every hyperelliptic curve over $K$ with all of its Weierstrass points defined over $K$ has infinitely many $K$-points. If, in addition, $K$ is not locally finite, then every elliptic curve over $K$ with all of its 2-torsion rational has infinite rank over $K$. These and similar results are deduced from the Hales-Jewett theorem.

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