Iwasawa theory for Galois extensions of number fields with restricted ramification and its applications

有限分枝数域伽罗瓦扩张的岩泽理论及其应用

• 批准号: 22740010
• 负责人: MIZUSAWA Yasushi
• 金额: $ 1.25万
• 依托单位: Nagoya Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740010/
• 关键词: 代数体; 岩澤理論; ガロア群

Galois extensions of number fields with restricted ramification contain a lot of important information in number theory, for example the difficulty of unique prime factorization of higher dimensional integers. We studied the relationship between a related open problem in Iwasawa theory and non幼ommutative structure of the Galois extensions, and we gave new explicit examples. Moreover, we studied an analogous problem in knot theory in order to obtain new evidence of an unsolved conjecture.

Galois extensions of number fields with restricted ramification contain a lot of important information in number theory, for example the difficulty of unique prime factorization of higher dimensional integers. We studied the relationship between a related open problem in Iwasawa theory and non explanatory structure of the Galois extensions, and we gave new explicit examples. Moreover, we studied an analogous problem in knot theory in order to obtain new evidence of an unsolved conjecture.

项目成果

ON THE IWASAWA INVARIANTS OF A LINK IN THE 3-SPHERE

论3-球内连接的岩泽不变量

• DOI: 10.2206/kyushujm.67.215
• 发表时间: 2013
• 期刊: Kyushu Journal of Mathematics
• 影响因子: 0.4
• 作者: Y.Mizusawa;M.Ozaki;Ryo Takahashi;門上晃久,水澤靖
• 通讯作者: 門上晃久,水澤靖

基本Z_p-拡大の馴分岐岩澤加群について

关于基本 Z_p 扩展的熟悉的 Iwasawa 模块

• 发表时间: 2010
• 作者: Y.Mizusawa;T.Itoh;M.Ozaki;Akira Ishii;Hideto Asashiba;Akira Ishii;石井亮;尾崎学;M. Kobayashi and M. Mase;Terai Naoki and Trung Ngo Viet;Hideto Asashiba;Naoki Terai and Ngo Viet Trung;伊藤剛司
• 通讯作者: 伊藤剛司

基本Zp拡大上の馴分岐pro-p拡大について

关于基本 Zp 扩展的自适应 Pro-p 扩展

• 发表时间: 2012
• 期刊: 第6回福岡整数論研究集会報告集
• 作者: Y.Mizusawa;M.Ozaki;Ryo Takahashi;門上晃久,水澤靖;Hikoe Enomoto and Naoya Enomoto;伊藤剛司,水澤靖
• 通讯作者: 伊藤剛司,水澤靖

On tame pro-p Galois groups over basic Z_p-extensions

基本 Z_p 扩展上的驯服 Pro-p 伽罗瓦群

• DOI: 10.1007/s00209-012-1048-2
• 发表时间: 2013
• 期刊: Math.Z.
• 作者: Y.Mizusawa;M.Ozaki
• 通讯作者: M.Ozaki

Iwasawa invariants of cyclic branched covers of links

链接循环分支覆盖的 Iwasawa 不变量

• 作者: 門上晃久;水澤靖
• 通讯作者: 水澤靖