On the torsion of elliptic curves and elliptic surfaces in characteristic
Author:
Andreas Schweizer
Journal:
Trans. Amer. Math. Soc. 357 (2005), 10471059
MSC (2000):
Primary 11G05, 14J27
Published electronically:
May 10, 2004
MathSciNet review:
2110432
Fulltext PDF Free Access
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Abstract: We study the extension generated by the coordinates of the torsion points of an elliptic curve over a function field of characteristic . If is a nonisotrivial elliptic surface in characteristic with a torsion section, then for our results imply restrictions on the genus, the gonality, and the rank of the base curve , whereas for such a surface can be constructed over any base curve . We also describe explicitly all occurring in the cases where the surface is rational or or the base curve is rational, elliptic or hyperelliptic.
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Additional Information
Andreas Schweizer
Affiliation:
Korea Institute for Advanced Study (KIAS), 20743 Cheongnyangni 2dong, Dong daemungu, Seoul 130722, Korea
Email:
schweiz@kias.re.kr
DOI:
http://dx.doi.org/10.1090/S0002994704035202
PII:
S 00029947(04)035202
Keywords:
Elliptic curve,
nonisotrivial elliptic surface,
$p$primary torsion,
uniform bound,
Hasse invariant,
Igusa curve,
gonality,
$K3$ surface
Received by editor(s):
August 5, 2002
Received by editor(s) in revised form:
August 25, 2003
Published electronically:
May 10, 2004
Article copyright:
© Copyright 2004
American Mathematical Society
