Fitting ideals in equivariant Iwasawa theory

In equivariant Iwasawa theory, the Iwasawa modules which we are interested in are slightly modified appropriately. While the modification prevents us from computing the Fitting ideals of the Iwasawa modules directly, Greither and Kurihara gave an explicit description of them in the most fundamental case.  In this talk, I will discuss a generalization of the algebraic theory behind the work of Greither and Kurihara, and applications of the generalization to other situations which appear in Iwasawa theory.