Properties of mapping class groups related to Galois representations
Properties of mapping class groups related to Galois representations
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
中文摘要
设κ_0是有限代数数域,κ_∞是与κ_0邻接所有单位根得到的域,L是κ_∞的最大未分支阿贝尔扩张。设κ_1是通过将ζ_4和ζ_p对所有奇素数p邻接到κ_0而得到的域,考虑Gal1(κ_∞/κ_0)的子群g=Gal(κ_∞/κ_1)。本文研究了半群(L/κ_∞)的结构和具有这种g-作用的理想类群C_∞.对于半群(L/κ_∞),我们证明了它作为完备群代数Z^[[g]]上的模,同构于Z^^[[g]]的可数拷贝数的直积.另一方面,理想类群C_∞是离散g-模。设κ_0为全实数,p为奇素数。设C_∞(P)^-表示C_∞)(P)在复共轭作用下的负部分。(栗原的结果表明加号部分是{0}。)一般地,对于一个PRO-pg-模X和所有p次方单位根的群W(P),设Hom(X,W(P))表示从X到W(P)的连续同态集。那么这自然是一个离散的g-模。对于C_∞(P)^-,我们证明了它与Hom(Π^∞_<;N=1>;Z_p[[g]],W(P))同构。(Z_p[[g]]:环Z_p上的完备群代数g。
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)
专著(0)
科研奖励(0)
会议论文
登录
查看更多内容
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
Homotopy types of the components of the spaces of embeddings of compact polyhedra into 2-manifolds
紧多面体嵌入2-流形的空间分量的同伦类型
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
Homotopy types of the components of spaces of embeddings of compact polyhedra into 2-manifolds
紧多面体嵌入2-流形的空间分量的同伦类型
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
Homotopy types of the components of spaces of embeddings of compact polyhedra into 2-manifolds.
紧多面体嵌入 2-流形的空间分量的同伦类型。
DOI:
--
发表时间:
期刊:
Topology and its applications (To appear)
影响因子:
--
作者:
[P.Lochak, H.Nakamura, L.Schneps, T.Yagasaki]
通讯作者:
T.Yagasaki
共 8 条
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:
Properties of mapping class groups related to Galois representations
-
批准号:09640033
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.73万
-
财政年份:1997
-
负责人:ASADA Mamoru
-
依托单位:
海外基金