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Properties of mapping class groups related to Galois representations

Properties of mapping class groups related to Galois representations
与伽罗瓦表示相关的映射类组的属性
批准号:
15540025
负责人:
ASADA Mamoru
金额:
$1.47万
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2003
资助国家:
日本
项目状态:
已结题
起止时间:
2003 至 2004

项目摘要

项目成果

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中文摘要
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英文摘要
Let κ_0 be a finite algebraic number field, κ_∞ be the field obtained by adjoining to κ_0 all roots of unity, and L be the maximal unramified abelian extension of κ_∞. Let κ_1 be the field obtained by adjoining ζ_4 and ζ_p for all odd prime p to κ_0 and consider the subgroup g=Gal(κ_∞/κ_1) of Gal(κ_∞/κ_0). In this research, we have investigated the structure of Gal(L/κ_∞) and the ideal class group C_∞ of κ_∞ with this g-action.As for Gal(L/κ_∞), we have shown that it is, as modules over the completed group algebra Z^^^[[g]], isomorphic to the direct pruduct of countable number of copies of Z^^^[[g]]. (Z^^^: the profinite completion of the ring of rational integers Z.)On the other hand, the ideal class group C_∞ is a discrete g-module. Assume that κ_0 is totally real and p is an odd prime. Let C_∞ (p)^- denote the minus part of C_∞)(p) under the action of the complex conjugation. (A result of Kurihara indicates that the plus part is {0}.) In general, for a pro-p g-module X and the group W(p) of all p-powerth roots of unity, let Hom(X,W(p)) denote the set of continuous homomorphisms from X to W(p). Then this is naturally a discrete g-module. As for C_∞(p)^-, we have shown that it is isomorphic to Hom(Π^∞_<N=1> Z_p[[g]], W(p)). (Z_p[[g]] : the completed group algebra g over the ring of p-adic integers Z_p.
期刊论文(20)
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会议论文
On the cyclotomic Galois action on the ideal class group of the maximal cyclotomic field (in Japanese).
关于最大分圆域的理想类群的分圆伽罗瓦作用(日语)。
DOI: --
发表时间: 2005
期刊: Proceeding of the conference Sendai mini symposium on Number Theory and Combinatorial Theory 2004
影响因子: --
作者: [朝田 衞, M.Asada]
通讯作者: M.Asada
DOI: --
发表时间:
期刊: Topology and its Applications in press
影响因子: --
作者: [P.Lochak, H.Nakamura, L.Schneps, T.Yagasaki]
通讯作者: T.Yagasaki
DOI: --
发表时间:
期刊: Topology and its applications (to appear)
影响因子: --
作者: [F.Maitani, H.Yamaguchi, T.Yagasaki]
通讯作者: T.Yagasaki
Eigenloci of 5 point configurations on the Riemann sphere and the Grothendieck-Teichmuller group
黎曼球和 Grothendieck-Teichmuller 群上 5 点配置的特征轨迹
DOI: --
发表时间:
期刊: Mathematical Journal of Okayama University (to appear)
影响因子: --
作者: [P.Lochak, H.Nakamura, L.Schneps]
通讯作者: L.Schneps
8
    Galois groups of unramified extensions over maximal cyclotomic fields
    • 批准号:
      22540019
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $1.25万
    • 财政年份:
      2010
    • 负责人:
      ASADA Mamoru
    • 依托单位:
    Galois groups of unramified extensions over maximal cyclotomic fields
    • 批准号:
      18540029
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $1.15万
    • 财政年份:
      2006
    • 负责人:
      ASADA Mamoru
    • 依托单位:
    Properties of mapping class groups related to Galois representations
    • 批准号:
      13640020
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.11万
    • 财政年份:
      2001
    • 负责人:
      ASADA Mamoru
    • 依托单位:
    Properties of mapping class groups rolated to Gdois representations
    • 批准号:
      11640026
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.3万
    • 财政年份:
      1999
    • 负责人:
      ASADA Mamoru
    • 依托单位:
    海外基金