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1 results

  • Height Uniformity for Algebraic Points on Curves

  • Su-Ion Ih
  • Journal:
    Compositio Mathematica / Volume 134 / Issue 1 / October 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 35-57
    Print publication:
    October 2002
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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.