Basic Structures of Function Field Arithmetic

The arithmetic of function fields over finite fields has been an area of extensive research for about two decades with many tantalizing results having recently been obtained. This book offers a self-contained introduction to basic concepts such as Drinfeld modules, T-modules, shtuka, exponentiation of ideals, and characteristic p L-functions and Gamma-functions in all their various manifestations. Insight from classical number theory, differential equations/algebra and algebraic geometry is presented whenever needed. Interesting unsolved problems are posed to the reader and a comprehensive list of references is included. All of this is presented to give the reader the basic tools to begin doing active research into this rapidly expanding area.