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 |
| 巻 | 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 |
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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
}
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 -