Lang's Height Conjecture and Szpiro's Conjecture

Details Lang's Height Conjecture and Szpiro's Conjecture Lang's Height Conjecture and Szpiro's Conjecture

2009-08-26

arxiv.org/abs/0908.3895v1

New York Journal of Math. 16 (2010), 1--12

Mathematics

Number Theory

12 pages

Scientific paper

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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