Drinfeld Modules over Finite Fields

Abstract

In this chapter we study Drinfeld modules defined over a finite field $$k= \mathbb {F}_{q^n}$$ . What distinguishes the theory of these Drinfeld modules from the general theory is that the Frobenius π := τ n commutes with every other element of $$k\!\left \{\tau \right \}$$ , hence A[π] is a subring of $$ \operatorname {\mathrm {End}}_k(\phi )$$ for any Drinfeld module ϕ; this simple observation is the starting point of the main results of this chapter.