Inductive construction of the p-adic zeta functions for noncommutative p-extensions of exponent p of totally real fields

研究成果: ジャーナルへの寄稿記事

2 引用 (Scopus)

抄録

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) noncommutative p-extension F∞ of a totally real number field F such that the finite part of its Galois groupGis a p-group of exponent p. We first calculate theWhitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative p-adic zeta function to certain congruences between abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne and Ribet's theory and a certain inductive technique. As an application we prove a special case of (the p-part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.

元の言語英語
ページ(範囲)247-305
ページ数59
ジャーナルDuke Mathematical Journal
158
発行部数2
DOI
出版物ステータス出版済み - 6 1 2011
外部発表Yes

Fingerprint

P-adic
Riemann zeta function
Exponent
Congruence
Galois
P-groups
Logarithm
Number field
Equivariant
Verify
Calculate
Algebra

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Inductive construction of the p-adic zeta functions for noncommutative p-extensions of exponent p of totally real fields. / Hara, Takashi.

:: Duke Mathematical Journal, 巻 158, 番号 2, 01.06.2011, p. 247-305.

研究成果: ジャーナルへの寄稿記事

@article{22d032e318ca4b3191154f4e2ed666d0,
title = "Inductive construction of the p-adic zeta functions for noncommutative p-extensions of exponent p of totally real fields",
abstract = "We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) noncommutative p-extension F∞ of a totally real number field F such that the finite part of its Galois groupGis a p-group of exponent p. We first calculate theWhitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative p-adic zeta function to certain congruences between abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne and Ribet's theory and a certain inductive technique. As an application we prove a special case of (the p-part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.",
author = "Takashi Hara",
year = "2011",
month = "6",
day = "1",
doi = "10.1215/00127094-1334013",
language = "English",
volume = "158",
pages = "247--305",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "2",

}

TY - JOUR

T1 - Inductive construction of the p-adic zeta functions for noncommutative p-extensions of exponent p of totally real fields

AU - Hara, Takashi

PY - 2011/6/1

Y1 - 2011/6/1

N2 - We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) noncommutative p-extension F∞ of a totally real number field F such that the finite part of its Galois groupGis a p-group of exponent p. We first calculate theWhitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative p-adic zeta function to certain congruences between abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne and Ribet's theory and a certain inductive technique. As an application we prove a special case of (the p-part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.

AB - We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) noncommutative p-extension F∞ of a totally real number field F such that the finite part of its Galois groupGis a p-group of exponent p. We first calculate theWhitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative p-adic zeta function to certain congruences between abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne and Ribet's theory and a certain inductive technique. As an application we prove a special case of (the p-part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.

UR - http://www.scopus.com/inward/record.url?scp=79959902068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959902068&partnerID=8YFLogxK

U2 - 10.1215/00127094-1334013

DO - 10.1215/00127094-1334013

M3 - Article

AN - SCOPUS:79959902068

VL - 158

SP - 247

EP - 305

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 2

ER -