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arXiv · 1612.04325

On the number of rational points on special families of curves over function fields

Douglas Ulmer·José Felipe Voloch
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Abstract

We construct families of curves which provide counterexamples for a uniform boundedness question. These families generalize those studied previously by several authors. We show, in detail, what fails in the argument of Caporaso, Harris, Mazur that uniform boundedness follows from the Lang conjecture. We also give a direct proof that these curves have finitely many rational points and give explicit bounds for the heights and number of such points.

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Douglas Ulmer, José Felipe Voloch. 2016-12-14. On the number of rational points on special families of curves over function fields. https://arxiv.org/abs/1612.04325

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