Integral points on elliptic curves over function fields of positive characteristic

被引:0
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作者
Pacheco, A
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D O I
10.1017/S0004972700032329
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let K be a one variable function field of genus g defined over an algebraically closed field Ic of characteristic p > 0. Let E/K be a non-constant elliptic curve. Denote by M-K the set of places of K and let S subset of M-K 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 R-S 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.
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页码:353 / 357
页数:5
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