Basic Properties of Drinfeld Modules

Abstract

A Drinfeld module over a field K, our principal object of study in this book, is a field K equipped with an action of the ring of polynomials $$\mathbb {F}_q[T]$$ , where $$\mathbb {F}_q[T]$$ acts via certain linearized polynomials in K[x]. In this chapter, we study the basic properties of Drinfeld modules which are valid over arbitrary fields. Later in the book we will be interested in the properties of Drinfeld modules defined over arithmetically interesting fields, such as finite fields, local fields, and global fields.