Some applications of the Hales-Jewett theorem to field arithmetic

被引：0
作者：
Bo-Hae Im
Michael Larsen
机构：
[1] Chung-Ang University,Department of Mathematics
[2] Indiana University,Department of Mathematics
来源：
Israel Journal of Mathematics | 2013年 / 198卷
关键词：
Elliptic Curve; Maximal Ideal; Elliptic Curf; Abelian Variety; Hyperelliptic Curve;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 an algebraic extension of a finite field, 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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页码：35 / 47
页数：12
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