UC San Diego

In this dissertation, we study the class modules associated to a Drinfeld module in certain infinite towers of function fields. We show that the inverse limit of these class modules is finitely generated and torsion as a module over the Iwasawa algebra. Using the Equivariant Tamagawa Number Formula for Drinfeld modules, we then propose an Iwasawa main conjecture for these modules which would precisely describe the Fitting ideal of their inverse limit as a module over the Iwasawa algebra.