Integral points on elliptic curves over function fields of positive characteristic

Source abstract

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 M K the set of places of K and let S ⊂ 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.