The ABC Conjecture Implies Vojta's Height Inequality for Curves

Following Elkies (Internat. Math. Res. Notices7 (1991) 99–109) and Bombieri (Roth's theorem and the abc-conjecture, preprint, ETH Zürich, 1994), we show that the ABC conjecture implies the one-dimensional case of Vojta's height inequality. The main geometric tool is the construction of a B...

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Veröffentlicht in:	Journal of number theory 2002-08, Vol.95 (2), p.289-302
1. Verfasser:	Van Frankenhuysen, Machiel
Format:	Artikel
Sprache:	eng
Schlagworte:	ABC conjecture Diophantine approximation effective Mordell Mordell's conjecture Roth's theorem the error term in the ABC conjecture type of an algebraic number Vojta's height inequality
Online-Zugang:	Volltext
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