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Integral points on elliptic curves over function fields of positive characteristic

Published online by Cambridge University Press:  17 April 2009

Amílcar Pacheco
Amílcar Pacheco
Affiliation:
Rua Guaiaquil 83, Cachambi, 20785-050 Rio de Janeiro, RJ, Brasil e-mail: [email protected]
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Abstract

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Let K be a one variable function field of genus g defined over an algebraically closed field k of characteristic p > 0. Let E/K be a non-constant elliptic curve. Denote by MK the set of places of K and let S ⊂ MK be a non-empty finite subset.

Mason in his paper “Diophantine equations over function fields” Chapter VI, Theorem 14 and Voloch in “Explicit p-descent for elliptic curves in characteristic p” Theorem 5.3 proved that the number of S-integral points of a Weiertrass equation of E/K defined over RS is finite. However, no explicit upper bound for this number was given. In this note, under the extra hypotheses that E/K is semi-stable and p > 3, we obtain an explicit upper bound for this number for a certain class of Weierstrass equations called S-minimal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 353 - 357
Copyright
Copyright © Australian Mathematical Society 1998

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