pith. sign in

arxiv: 1206.7047 · v1 · pith:F355CXGKnew · submitted 2012-06-29 · 🧮 math.NT · math.DS

Torsion points in families of Drinfeld modules

classification 🧮 math.NT math.DS
keywords torsiondrinfeldkbarmodulespointsthenadditionalgebraic
0
0 comments X
read the original abstract

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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.