Uniform boundedness for rational points

@article{Pacelli1996UniformBF,
  title={Uniform boundedness for rational points},
  author={Patricia L. Pacelli},
  journal={Duke Mathematical Journal},
  year={1996},
  volume={88},
  pages={77-102}
}
We extend an earlier result by Dan Abramovich, showing that a conjecture of S. Lang's implies the existence of a uniform bound on the number of $K$-rational points over all smooth curves of genus $g$ defined over $K$, where $K$ is any number field of fixed degree $d$, and $g$ is an integer greater than 1. The bound depends only on the genus $g$ and the degree of the number field $K$. 
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Uniformity of rational points
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