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

研究成果: Contribution to journalArticle査読

2 被引用数 (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.

本文言語英語
ページ(範囲)247-305
ページ数59
ジャーナルDuke Mathematical Journal
158
2
DOI
出版ステータス出版済み - 6 1 2011
外部発表はい

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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