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Inductive construction of the p-adic zeta functions for non-commutative p-extensions of exponent p of totally real fields
https://doi.org/10.15083/00004044
https://doi.org/10.15083/0000404457949e95-3867-4956-8e74-6f0a5a56522d
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HaraT_23_3_PhD_a.pdf (1.8 MB)
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HaraT_23_3_PhD_b.pdf (195.1 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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公開日 | 2012-10-23 | |||||
タイトル | ||||||
タイトル | Inductive construction of the p-adic zeta functions for non-commutative p-extensions of exponent p of totally real fields | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_46ec | |||||
タイプ | thesis | |||||
ID登録 | ||||||
ID登録 | 10.15083/00004044 | |||||
ID登録タイプ | JaLC | |||||
その他のタイトル | ||||||
その他のタイトル | 総実代数体の羃指数p型非可換p拡大に対するp-進ゼータ関数の帰納的構成 | |||||
著者 |
Hara, Takashi
× Hara, Takashi |
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著者別名 | ||||||
識別子 | 9351 | |||||
識別子Scheme | WEKO | |||||
姓名 | 原, 隆 | |||||
著者所属 | ||||||
著者所属 | 東京大学大学院数理科学研究科 | |||||
著者所属 | ||||||
著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
Abstract | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We construct the p-adic zeta function for a one-dimensional(as a p-adic Lie extension) non-commutative p-extension F∞ of a totallyreal number field F such that the finite part of its Galois group G is ap-group of exponent p. We first calculate the 'Whitehead groups of theIwasawa algebra Λ(G) and its canonical Ore localisation Λ(G)s by usingOliver-Taylor's theory of integral logarithms. This calculation reducesthe existence of the non-commutative p-adic zeta function to certain congruencesbetween abelian p-adic zeta pseudomeasures. Then we finallyverify these congruences by using Deligne-Ribet's theory and a certaininductive technique. As an application we shall prove a special caseof (the p-part of) the non-commutative equivariant Tamagawa numberconjecture for critical Tate motives. | |||||
書誌情報 | 発行日 2011-03-24 | |||||
日本十進分類法 | ||||||
主題 | 410 | |||||
主題Scheme | NDC | |||||
学位名 | ||||||
学位名 | 博士(数理科学) | |||||
学位 | ||||||
値 | doctoral | |||||
学位分野 | ||||||
Mathematical Sciences (数理科学) | ||||||
学位授与機関 | ||||||
学位授与機関名 | University of Tokyo (東京大学) | |||||
研究科・専攻 | ||||||
Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
学位授与年月日 | ||||||
学位授与年月日 | 2011-03-24 | |||||
学位授与番号 | ||||||
学位授与番号 | 甲第27193号 | |||||
学位記番号 | ||||||
博数理第374号 |