UC San Diego

In this dissertation we prove a new equivariant main conjecture in Iwasawa theory associated to the cyclotomic Z_p−extension of a CM number field over a totally real number field. Our object of interest ∇^T_S (H^∞)−p is the projective limit of certain p−adic Ritter-Weiss modules which is class field theoretically significant and has nice cohomological properties. Our main result is a number field analogue of the recent results of Bley and Popescu [14] on a certain Drinfeld modular Iwasawa tower of function fields. As an application, we compute the 0-th Fitting ideal of a naturally arising Iwasawa module over the relevant equivariant Iwasawa algebra.