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Height Uniformity for Algebraic Points on Curves

Published online by Cambridge University Press:  04 December 2007

Su-Ion Ih
Su-Ion Ih
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, IL 60607, U.S.A. [email protected]
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Abstract

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We recall the main result of L. Caporaso, J. Harris, and B. Mazur's 1997 paper of ‘Uniformity of rational points.’ It says that the Lang conjecture on the distribution of rational points on varieties of general type implies the uniformity for the numbers of rational points on curves of genus at least 2. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights.

Keywords

ample divisorbig divisorcanonical divisorfiber productheightheight zeta functionsymmetric productvariety of general typeVojta conjecture
Type
Research Article
Information
Compositio Mathematica , Volume 134 , Issue 1 , October 2002 , pp. 35 - 57
Copyright
© 2002 Kluwer Academic Publishers