Computing Fitting ideals of Iwasawa modules

This paper determines, in an equivariant sense, the Fitting ideals of several Iwasawa modules including the most canonical one. The connection between the modules themselves, which are usually not of finite projective dimension, and the required auxiliary modules of finite projective dimension is made rather explicit. The resulting Fitting ideals look like Stickelberger ideals, and there is a close relation with recent work of Kurihara. As an application we obtain new evidence in favor of the Brumer-Stark conjecture.