Non-commutative I wa sawa theory

非交换伊瓦萨瓦理论

• 批准号: 16340005
• 负责人: KATO Kazuya
• 金额: $ 8.93万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340005/
• 关键词: Non-commutafice Iwasawa theroy; Iwasawa theroy; Iwasawa algebra; K_1-group; P-adic veta function; Hodge structure; reglator; Galois group; Hodge構造; 退化; P進Hodge構造; ゼータ関数; regnlator; height pairing; 非可損岩澤理論; 総実代数体; 保型形式; 主予想; アーベル多様体; セルマ

With J.Coaten, T. Fukaya, R. Sujatha, and O. Verjakob, the head investigator K. Kato formulated "main conjecture" of non-commutatire Iwasawa theory. K. Kato obtained progresses in attacking this main conjecture. The key approach started by him is the study of K_1 of non-commutatire Iwasawa algebras. This opened the way to reduce non-commutatire Iwasawa theory, to Commutatire Iwasawa theory and congruences between various commutatire p-adic zeta functions. In the case the Galois group is of Heisenberg type, K.Kato proved the main conjecture in the non-commutatire Iwasawa theory of non-commutatire Iwasawa theory of totally real fields.With S. Usui and C. Nakayama, K. kato studied degeneration of mixed Hodge structure, and obtained the mixed Hodge version of SL(2)-orbit thesrem. He obtained the p-adic version with. S. Bloch, K, kato obtained results on the behavior of regulator in degeneration and showed that zeta values appear there. This is a hew direction of Iwasawa theory.

与J.Coaten，T.福谷河Sujatha和O. Verjakob，首席调查员K。加藤提出了非对易岩泽理论的“主要猜想”。K. Kato在对这一主要猜想的攻击中取得了进展。他开创的关键方法是研究非交换岩泽代数的K_1。这开辟了道路，以减少非commutatire岩泽理论，以Commutatire岩泽理论和各种commutatire p进zeta函数之间的同余关系。K.Kato在Galois群为Heisenberg型的情况下证明了全真实的域的非对易岩泽理论中的主要猜想。和C. Nakayama，K. kato研究了混合Hodge结构的退化，得到了SL（2）-轨道的混合Hodge形式.他得到了p-adic版本。S. Bloch，K，Kato获得了调节剂在退化中的行为的结果，并表明zeta值出现在那里。这是岩泽理论的一个新方向。

项目成果

K_1 of some non-commufative completed group rings

K_1 一些非交换完成群环

• 发表时间: 2005
• 期刊: K-theory 34
• 作者: Kato;Kazuya
• 通讯作者: Kazuya

K_1 of same non-commutative complete group rings

K_1 个相同的非交换完全群环

• 发表时间: 2005
• 期刊: K-theory 34
• 作者: K. Matsumoto;H. Tsumura;Kazuya Kato
• 通讯作者: Kazuya Kato

Ramification theory for ranieties over a perfect field

完美域上的兰尼斯特的分支理论

• 期刊: Amnals of Math (掲載確定)
• 作者: Kato;Kazuya; Saito;Takeshi
• 通讯作者: Takeshi

Analytic log Picard varieties

解析对数 Picard 簇

• 期刊: Nagaya Math. J (掲載確定)
• 作者: Kajiwara;Takeshi; Kato;Kazuya Nakayama;Chikara
• 通讯作者: Chikara

K_1 of some non-commutative Iwasawa algebras

一些非交换岩泽代数的 K_1

• 期刊: K-theory (発表予定)
• 作者: K.Matsumoto;A.Sankaranarayanan;Kazuya Kato
• 通讯作者: Kazuya Kato