标题： 族中的挠点 显示英文标题

标题： Torsion points in families of Drinfeld modules

摘要： 设$\Phi^\l$是在特征为$p$的域$K$上定义的德林模块的代数族，并设$\bfa,\bfb\in K[\l]$。 假设对于所有$\l$，$\bfa(\l)$和$\bfb(\l)$都不是$\Phi^\l$的挠点。 如果存在无限多个$\l\in\Kbar$使得对于$\Phi^\l$，$\bfa(\l)$和$\bfb(\l)$都是扭点，则我们证明对于每个$\l\in\Kbar$，当且仅当$\bfb(\l)$对于$\Phi^\l$是扭点时，$\bfa(\l)$对于$\Phi^\l$是扭点。 在情况$\bfa,\bfb\in K$中，我们进一步证明$\bfa$和$\bfb$必须是$\Fpbar$-线性相关的。 显示英文摘要

摘要： Let $\Phi^\l$ be an algebraic family of Drinfeld modules defined over a field $K$ of characteristic $p$, and let $\bfa,\bfb\in K[\l]$. Assume that neither $\bfa(\l)$ nor $\bfb(\l)$ is a torsion point for $\Phi^\l$ for all $\l$. If there exist infinitely many $\l\in\Kbar$ such that both $\bfa(\l)$ and $\bfb(\l)$ are torsion points for $\Phi^\l$, then we show that for each $\l\in\Kbar$, we have that $\bfa(\l)$ is torsion for $\Phi^\l$ if and only if $\bfb(\l)$ is torsion for $\Phi^\l$. In the case $\bfa,\bfb\in K$, then we prove in addition that $\bfa$ and $\bfb$ must be $\Fpbar$-linearly dependent.