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arXiv · 0908.3895

Lang's Height Conjecture and Szpiro's Conjecture

Joseph H. Silverman
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Abstract

It is known that Szpiro's conjecture, or equivalently the ABC-conjecture, implies Lang's conjecture giving a uniform lower bound for the canonical height of nontorsion points on elliptic curves. In this note we show that a significantly weaker version of Szpiro's conjecture, which we call "prime-depleted," suffices to prove Lang's conjecture.

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Joseph H. Silverman. 2009-08-26. Lang's Height Conjecture and Szpiro's Conjecture. https://arxiv.org/abs/0908.3895

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