On Isogeny Characters of Drinfeld Modules of Rank Two

Abstract

In this paper, we study cyclic torsion subgroups of Drinfeld Fq[T]- modules of rank two over Fq(T) via isogeny characters associated to them. Among other things, we prove that such Drinfeld Fq[T]-modules do not have a cyclic p-torsion subgroup defined over Fq(T) under various conditions, where p is a maximal ideal of Fq[T]. We also obtain some unconditional results.