  A uniform bound of intersection multiplicities of curves and divisors on
abelian varieties is proved by algebraic geometric methods. It extends and
improves a result obtained by A. Buium with a different method based on
Kolchin's differential algebra. The problem is modeled after the abc-Conjecture
of Masser-Oesterle for abelian varieties over the function field of a curve. As
an application a finiteness theorem is proved for maps from a curve into an
abelian variety omitting an ample divisor.
