We use the notion of non-commutative Fitting invariants to give a reformulation of the equivariant Iwasawa main conjecture (EIMC) attached to an extension F/K of totally real elds with Galois group G, where K is a global number eld and G is a p-adic Lie group of dimension 1 for an odd prime p. We attach to each nite Galois CM-extension L/K with Galois group G a module SKu(L/K) over the center o...

Let G be a pro-p p-adic analytic group, thought of as a closed subgroup of GLN (Zp), and let Σ be a closed subgroup of G. Write Λ for the completed group algebra Zp[[G]] and let M be a finitely generated Λ-module. Let G = G ⊃ G ⊃ G ⊃ . . . be the descending sequence of principal congruence subgroups of G; write Gn for the quotient G/G and Σn for the image of Σ in Gn. Write Mn for the coinvarian...

Abstract We completely calculate the Fitting ideal of classical p -ramified Iwasawa module for any abelian extension K / k totally real fields, using shifted ideals recently developed by second author. This generalizes former results where we had to assume that only -adic places may ramify in . One important ingredients is computation some complexes appropriate derived categories.

For an odd prime number p, we study the of generators unramified Iwasawa modules maximal multiple ℤ p -extensions over algebra. In our previous paper, under several assumptions for imaginary quadratic field, obtained a necessary and sufficient condition cyclicity module The present work provides computational methods numerical examples that are cyclic as We remark do not require assumption Gree...

Given a p-adic field K and nilpotent uniform pro-p group G, we prove that all primitive ideals in the K-rational Iwasawa algebra KG are maximal, can be reduced to particular standard form. Setting L as associated Zp-Lie of our approach is study action on Dixmier module D(?)ˆ over affinoid envelope U(L)ˆK, annihilators modules this

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 de...