### Bounds for the canonical height and integral points on elliptic curves over function fields, by Amilcar Pacheco

This paper has now appeared in Bulletin of the Australian Mathematical Society 58 (1998),
353-357 with the title `Integral points on elliptic curves over function
fields of positive characteristic' and so the dvi version has been removed.
In this paper we give a lower bound for the canonical
height of non-torsion points of an elliptic curve over
a function field of any characteristic in terms of the
corresponding j-map, the genus of the function field
and the discriminant of the elliptic curve. This is an
analogue of a result of Hindry-Silverman ["The canonical
height and integral points on elliptic curves,
Invent. Math., 1988] for an elliptic curve over a
function field of characteristic zero. It uses
Szpiro's theorem on the discriminant of elliptic
curves over function fields. We can improve their
bound in the cases of the univesal elliptic curves
over certain modular curves. Moreover we give a
geometric condition which justifies such improvement
and give examples in which it is fulfilled. Finally
this result, together with a bound for the torsion
subgroup of such elliptic curves and an upper bound
for the height of integral points, give a bound for
the number of integral points of a Weiertrass equation.

Amilcar Pacheco <amilcar@impa.br>