Fitting invariants in equivariant Iwasawa theory

The main conjectures in Iwasawa theory predict the relationship between modules and $p$-adic $L$-functions. Using a certain proved formulation of conjecture, Greither Kurihara described explicitly (initial) Fitting ideals for cyclotomic $\mathbb{Z}_p$-extensions finite abelian extensions totally real fields. In this paper, we generalize algebraic behind their work by developing “shifts invariants.” As applications to theory, obtain noncommutative version two-variable Kurihara.