Lang's Height Conjecture and Szpiro's Conjecture
Number Theory
2011-05-30 v1 Algebraic Geometry
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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Cite
@article{arxiv.0908.3895,
title = {Lang's Height Conjecture and Szpiro's Conjecture},
author = {Joseph H. Silverman},
journal= {arXiv preprint arXiv:0908.3895},
year = {2011}
}
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12 pages