Lang's height conjecture and Szpiro's conjecture

摘要

It is known that Szpiro's conjecture, or equivalently theABC-conjecture, implies Lang's conjecture giving a uniform lowerbound for the canonical height of nontorsion points on ellipticcurves. In this note we show that a significantly weaker version ofSzpiro's conjecture, which we call "prime-depleted,'' suffices toprove Lang's conjecture.