VOL. 86 | 2020 The second syzygy of the trivial G-module, and an equivariant main conjecture
Chapter Author(s) Cornelius Greither, Masato Kurihara, Hibiki Tokio
Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji
Adv. Stud. Pure Math., 2020: 317-349 (2020) DOI: 10.2969/aspm/08610317

Abstract

For a finite abelian p-extension K/k of totally real fields and the cyclotomic Zp-extension K/K, we prove a strong version of an equivariant Iwasawa main conjecture by determining completely the Fitting ideal over Zp[[Gal(K/k)]] of the classical Iwasawa module XK,S, which is the Galois group of the maximal pro-p abelian S-ramified extension of K, where S contains all ramified primes in K/k. To do this, we prove a conjecture which was proposed in a previous paper by the first and second author, concerning the minors of a relation matrix for the second syzygy module of the trivial module Z over a suitable group ring.

Information

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

Digital Object Identifier: 10.2969/aspm/08610317

Subjects:
Primary: 11R23 , 13D02 , 15A15

Keywords: Fitting ideal , Iwasawa module

Rights: Copyright © 2020 Mathematical Society of Japan

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