New development of Iwasawa theory and its applications

岩泽理论及其应用的新进展

• 批准号: 21340012
• 负责人: KURIHARA Masato
• 金额: $ 6.66万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21340012/
• 关键词: 整数論; セルマー群; イデアル類群; 岩澤理論; Tate Shafarevich群; Selmer 群; Fitting イデアル; 国際研究者交流; ドイツ：イギリス; Selmer群; Fittingイデアル; イギリス; 岩澤主予想; 楕円曲線; イギリス:アメリカ:韓国; カナダ:中国:アメリカ

We studied and obtained a refinement of the usual Iwasawa theory for general p-adic representations. In particular, for an elliptic curve over the rational number field with good ordinary reduction at p, assuming the main conjecture and the non-degeneracy of the p-adic height pairing, we proved a structure theorem for the p-component of the Selmer group of the curve. This theorem describes the structure of the Selmer group as an abelian group by analytic elements which come from modular symbols, so from the L-values. We also constructed a theory of Euler system and Kolyvagin system of Gauss sum type.For a CM-extension, we studied both theoretically and numerically a problem that the Stickelberger element is in the Fitting ideal of the dual of the ideal class group.

我们研究并获得了对普通P-ADIC代表的通常的Iwasawa理论的改进。特别是，对于在P AD P-Adic高度配对的主要猜想和非分类的合理数字字段上具有良好普通降低的椭圆曲线，我们证明了Selmer组P组件的结构定理曲线。该定理通过来自模块化符号的分析元素将Selmer组的结构描述为Abelian群体，因此来自L值。我们还构建了高斯总和的欧拉系统和kolyvagin系统的理论。对于cm延伸，我们从理论和数字上研究了一个问题，即Stickelberger元素在理想类群体的双重理想中属于理想的理想。

项目成果

Ideal class groups of CM-fields with non-cyclic Galois action

具有非循环伽罗瓦作用的 CM 域的理想类群

• 发表时间: 2012
• 期刊: Tokyo Journal of Mathematics
• 影响因子: 0.6
• 作者: Tetsuro Okuyama;Tomoyuki Wada;Masato Kurihara and Takashi Miura
• 通讯作者: Masato Kurihara and Takashi Miura

Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences

涉及连分数且由线性递推生成的某些级数的代数独立性的条件

• 发表时间: 2009
• 期刊: Journal of Number Theory 129
• 作者: Krupchyk;K; lLassas;Matti; Uhlmann;G.;Taka-aki Tanaka
• 通讯作者: Taka-aki Tanaka

Iwasawa lambda-invariants and congruence of Galois representations

Iwasawa lambda 不变量和伽罗瓦表示的同余

• 发表时间: 2011
• 期刊: Journal of the Ramanujan Math. Society
• 作者: M.Monshita;Y.Terashima;Y. Yoshino and T. Yoshizawa;Shigeo Kositani;Yoshitaka Hachimori
• 通讯作者: Yoshitaka Hachimori

Stickelberger ideals and Fitting ideals of class groups for abelian number fields

阿贝尔数域的斯蒂克伯格理想和类群拟合理想

• 发表时间: 2010
• 期刊: Mathematische Annalen (http://www.springer.com/mathematics/journal/208にてOnline First版
• 作者: Masato Kurihara;Takashi Miura
• 通讯作者: Takashi Miura

On stronger versions of Brumer's conjecture

关于布鲁默猜想的更强版本

• 发表时间: 2012
• 期刊: Tokyo Journal of Mathematics
• 影响因子: 0.6
• 作者: Hiroshi Kawakami;Akane Nakamura;Hidetaka Sakai;H.Nakamura;T.Ikeda;平野恵子・高橋信行・苅田知則;Maciej Karpicz;権 梅蘭・竹内 嘉恵・渡辺 春奈・上村 誠也・久津間 祐貴・長崎 勤;Masato Kurihara
• 通讯作者: Masato Kurihara