Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Applications of the Hales-Jewett Theorem to Field Arithmetic   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.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org