SOME APPLICATIONS OF THE HALES-JEWETT THEOREM TO FIELD ARITHMETIC

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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
Publisher
HEBREW UNIV MAGNES PRESS
Issue Date
2013-11
Language
English
Article Type
Article
Keywords

MORDELL-WEIL GROUPS; ELLIPTIC-CURVES; ABELIAN-VARIETIES; HEEGNER POINTS; RANK

Citation

ISRAEL JOURNAL OF MATHEMATICS, v.198, no.1, pp.35 - 47

ISSN
0021-2172
DOI
10.1007/s11856-013-0009-8
URI
http://hdl.handle.net/10203/213001
Appears in Collection
MA-Journal Papers(저널논문)
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