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Joseph H. Silverman
Lang's height conjecture and Szpiro's conjecture view print
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| Published: |
April 22, 2010
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| Keywords: |
elliptic curve, canonical height, Szpiro conjecture, Lang conjecture |
| Subject: |
Primary: 11G05; Secondary: 11G50, 11J97, 14H52 |
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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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| Acknowledgements
The author's research partially supported by NSF grants DMS-0650017 and DMS-0854755.
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| Author information
Mathematics Department, Box 1917 Brown University, Providence, RI 02912 USA
jhs@math.brown.edu
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