Heights and singular moduli of Drinfeld modules

Abstract

Let $q$ be an odd number and $q>5$, and ${\mathbb{F}}_q$ be a finite field of $q$ elements. We prove that at most finitely many singular moduli of rank 2 ${\mathbb{F}}_q[t]$-Drinfeld modules are algebraic units. In particular, we develop some techniques of heights of Drinfeld modules to approach it.

24 pages