D\'ecompte dans une conjecture de Lang sur les corps de fonctions : cas des courbes

摘要

Let $X$ be a genus $d$ curve with $d\geq 2$ defined over a global functionfield $K$ of characteristic $p>0$ with $p>2d+1$. Suppose $X$ non-isotrivial.Let $\Gamma$ be a sub-group of $J(K_s)$, where $J$ is the jacobian of $X$ and$K_s$ is a separable closure of $K$, verifying $\Gamma/p \Gamma$ finite. Thenone shows that $X\cap \Gamma$ has finite cardinal and one provides an explicitupper bound. This generalizes a result of Buium and Voloch.