VOL. 86 | 2020 Fitting invariants in equivariant Iwasawa theory
Takenori Kataoka

Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji

Adv. Stud. Pure Math., 2020: 413-465 (2020) DOI: 10.2969/aspm/08610413


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


Published: 1 January 2020
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.2969/aspm/08610413

Primary: 11R23 , 16E05

Keywords: Fitting invariants , Iwasawa modules , Tate sequences

Rights: Copyright © 2020 Mathematical Society of Japan


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