On stronger versions of brumer’s conjecture

研究成果: Article

3 引用 (Scopus)

抄録

Let k be a totally real number field and L a CM-field such that L/k is finite and abelian. In this paper, we study a stronger version of Brumer’s conjecture that the Stickelberger element times the annihilator of the group of roots of unity in L is in the Fitting ideal of the ideal class group of L, and also study the dual version. We mainly study the Teichmüller character component, and determine the Fitting ideal in a certain case. We will see that these stronger versions hold in a certain case. It is known that the stronger version (SB) does not hold in general. We will prove in this paper that the dual version (DSB) does not hold in general, either.

元の言語English
ページ(範囲)407-428
ページ数22
ジャーナルTokyo Journal of Mathematics
34
発行部数2
DOI
出版物ステータスPublished - 2017 1 1

Fingerprint

CM-field
Ideal Class Group
Annihilator
Roots of Unity
Number field
Character

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

On stronger versions of brumer’s conjecture. / Kurihara, Masato.

:: Tokyo Journal of Mathematics, 巻 34, 番号 2, 01.01.2017, p. 407-428.

研究成果: Article

@article{f8b97d0bf2c8410984dfa5142f1f5284,
title = "On stronger versions of brumer’s conjecture",
abstract = "Let k be a totally real number field and L a CM-field such that L/k is finite and abelian. In this paper, we study a stronger version of Brumer’s conjecture that the Stickelberger element times the annihilator of the group of roots of unity in L is in the Fitting ideal of the ideal class group of L, and also study the dual version. We mainly study the Teichm{\"u}ller character component, and determine the Fitting ideal in a certain case. We will see that these stronger versions hold in a certain case. It is known that the stronger version (SB) does not hold in general. We will prove in this paper that the dual version (DSB) does not hold in general, either.",
author = "Masato Kurihara",
year = "2017",
month = "1",
day = "1",
doi = "10.3836/tjm/1327931394",
language = "English",
volume = "34",
pages = "407--428",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "2",

}

TY - JOUR

T1 - On stronger versions of brumer’s conjecture

AU - Kurihara, Masato

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Let k be a totally real number field and L a CM-field such that L/k is finite and abelian. In this paper, we study a stronger version of Brumer’s conjecture that the Stickelberger element times the annihilator of the group of roots of unity in L is in the Fitting ideal of the ideal class group of L, and also study the dual version. We mainly study the Teichmüller character component, and determine the Fitting ideal in a certain case. We will see that these stronger versions hold in a certain case. It is known that the stronger version (SB) does not hold in general. We will prove in this paper that the dual version (DSB) does not hold in general, either.

AB - Let k be a totally real number field and L a CM-field such that L/k is finite and abelian. In this paper, we study a stronger version of Brumer’s conjecture that the Stickelberger element times the annihilator of the group of roots of unity in L is in the Fitting ideal of the ideal class group of L, and also study the dual version. We mainly study the Teichmüller character component, and determine the Fitting ideal in a certain case. We will see that these stronger versions hold in a certain case. It is known that the stronger version (SB) does not hold in general. We will prove in this paper that the dual version (DSB) does not hold in general, either.

UR - http://www.scopus.com/inward/record.url?scp=85017393031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017393031&partnerID=8YFLogxK

U2 - 10.3836/tjm/1327931394

DO - 10.3836/tjm/1327931394

M3 - Article

AN - SCOPUS:85017393031

VL - 34

SP - 407

EP - 428

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 2

ER -