naa a22 4500 510782310 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0009-8 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0009-8 Some applications of the Hales-Jewett theorem to field arithmetic [Elektronische Daten] [Bo-Hae Im, Michael Larsen] 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. Hebrew University Magnes Press, 2013 Im Bo-Hae Department of Mathematics, Chung-Ang University, 221, Heukseok-dong, Dongjak-gu, 156-756, Seoul, South Korea aut Larsen Michael Department of Mathematics, Indiana University, 47405, Bloomington, Indiana, USA aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 35-47 0021-2172 198:1<35 2013 198 11856 https://doi.org/10.1007/s11856-013-0009-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0009-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Im Bo-Hae Department of Mathematics, Chung-Ang University, 221, Heukseok-dong, Dongjak-gu, 156-756, Seoul, South Korea aut NATIONALLICENCE 700 1- Larsen Michael Department of Mathematics, Indiana University, 47405, Bloomington, Indiana, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 35-47 0021-2172 198:1<35 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer