東京大学大学院数理科学研究科
Graduate School of Mathematical Sciences, The University of Tokyo
Abstract
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.
発行年
2011-03-24
日本十進分類法
410
学位名
博士(数理科学)
学位
doctoral
学位分野
Mathematical Sciences (数理科学)
学位授与機関
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
2011-03-24
学位授与番号
甲第27193号
学位記番号
博数理第374号
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Inductive construction of the p-adic zeta functions for non-commutative p-extensions of exponent p of totally real fields
HaraT_23_3_PhD_a.pdf
(1.83MB)
