Fitting ideals of iwasawa modules and of the dual of class groups

Cornelius Greither, Masato Kurihara

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we study some problems related to a refinement of Iwasawa theory, especially questions about the Fitting ideals of several natural Iwasawa modules and of the dual of the class groups, as a sequel to our previous papers [8], [3]. Among other things, we prove that the annihilator of Zp(1) times the Stickelberger element is not in the Fitting ideal of the dualized Iwasawa module if the p-component of the bottom Galois group is elementary p-abelian with p-rank 4. Our results can be applied to the case that the base field is Q.

Original languageEnglish
Pages (from-to)619-642
Number of pages24
JournalTokyo Journal of Mathematics
Volume39
Issue number3
Publication statusPublished - 2017 Mar 1

Fingerprint

Class Group
Iwasawa Theory
P-rank
Module
Annihilator
Galois group
Thing
Refinement

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fitting ideals of iwasawa modules and of the dual of class groups. / Greither, Cornelius; Kurihara, Masato.

In: Tokyo Journal of Mathematics, Vol. 39, No. 3, 01.03.2017, p. 619-642.

Research output: Contribution to journalArticle

@article{8b5f6c6300e94acc929ecccde1f1e647,
title = "Fitting ideals of iwasawa modules and of the dual of class groups",
abstract = "In this paper we study some problems related to a refinement of Iwasawa theory, especially questions about the Fitting ideals of several natural Iwasawa modules and of the dual of the class groups, as a sequel to our previous papers [8], [3]. Among other things, we prove that the annihilator of Zp(1) times the Stickelberger element is not in the Fitting ideal of the dualized Iwasawa module if the p-component of the bottom Galois group is elementary p-abelian with p-rank 4. Our results can be applied to the case that the base field is Q.",
author = "Cornelius Greither and Masato Kurihara",
year = "2017",
month = "3",
day = "1",
language = "English",
volume = "39",
pages = "619--642",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "3",

}

TY - JOUR

T1 - Fitting ideals of iwasawa modules and of the dual of class groups

AU - Greither, Cornelius

AU - Kurihara, Masato

PY - 2017/3/1

Y1 - 2017/3/1

N2 - In this paper we study some problems related to a refinement of Iwasawa theory, especially questions about the Fitting ideals of several natural Iwasawa modules and of the dual of the class groups, as a sequel to our previous papers [8], [3]. Among other things, we prove that the annihilator of Zp(1) times the Stickelberger element is not in the Fitting ideal of the dualized Iwasawa module if the p-component of the bottom Galois group is elementary p-abelian with p-rank 4. Our results can be applied to the case that the base field is Q.

AB - In this paper we study some problems related to a refinement of Iwasawa theory, especially questions about the Fitting ideals of several natural Iwasawa modules and of the dual of the class groups, as a sequel to our previous papers [8], [3]. Among other things, we prove that the annihilator of Zp(1) times the Stickelberger element is not in the Fitting ideal of the dualized Iwasawa module if the p-component of the bottom Galois group is elementary p-abelian with p-rank 4. Our results can be applied to the case that the base field is Q.

UR - http://www.scopus.com/inward/record.url?scp=85017393073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017393073&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85017393073

VL - 39

SP - 619

EP - 642

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 3

ER -