On the -torsion of elliptic curves and elliptic surfaces in characteristic

Author:
Andreas Schweizer

Journal:
Trans. Amer. Math. Soc. **357** (2005), 1047-1059

MSC (2000):
Primary 11G05, 14J27

DOI:
https://doi.org/10.1090/S0002-9947-04-03520-2

Published electronically:
May 10, 2004

MathSciNet review:
2110432

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Abstract | References | Similar Articles | Additional Information

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 non-isotrivial 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), 207-43 Cheongnyangni 2-dong, Dong- daemun-gu, Seoul 130-722, Korea

Email:
schweiz@kias.re.kr

DOI:
https://doi.org/10.1090/S0002-9947-04-03520-2

Keywords:
Elliptic curve,
non-isotrivial 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