Iwasawa theory of Harse zeta functions

岩泽 Harse zeta 函数理论

• 批准号: 11440003
• 负责人: KATO Kazuya
• 金额: $ 6.59万
• 依托单位: KYOTO UNIVERSITY (2001)The University of Tokyo (1999-2000)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440003/
• 关键词: Harse zeta function; moduler forms; Iwasawa theory; abelian variety; BSD conjecture; conductor; log geometry; Birch Swinnerton-Dyer予想; Hodge構造; log代数多様体; 退化; 導手公式; SL(2)-orbit; 代数体; エタール・コホモロジー; 微分加群; 対数的アーベル多様体; コンパクト化; 極小モデル; ホッジ構造

Concerning Iwasawa theory of moduar forms, I completed the preprint "p-adic Hoclge theory and values of zeta funcions of moduar forms" (244 pages). In this paper, I proved the half of Iwasawa main conjecture for modular forms. (Half means one 【less than or equal】 in the conjecture which has the form of the equality "zeta side"="arithmetic group side.)As an application I obtained results on BSD confectures on elliptic curves over rational number field.Concerning BSD 'cong' for abelian varieties over global fields of poeetre characteristic, I proved it assuming the fimteness of Take-Shaturevich group (with F. Trihen).I proved Blocn's conductor formula by the joint work with Takeshi Saito, This is related also to Harse zeta functions.I obtained results on log Hodge theory and on log abelian varieties by using the method of log geometry.

关于岩泽的模形式理论，我完成了预印本“p-adic Hoclge理论和模形式zeta函数的值”（244页）。本文证明了关于模形式的岩泽主猜想的一半。(Half在猜想中的意思是一个[小于或等于]，它具有等式“zeta side”=“算术群side”的形式。作为应用，我得到了有理数域上椭圆曲线上BSD簇的结果，关于整体Poeetre特征域上交换簇的BSD“cong”，在Take-Shaturevich群（F. Trihen），与斋藤武共同证明了Blocn的导体公式，这也与Harse zeta函数有关，用对数几何的方法得到了log Hodge理论和log Abel簇的结果。

项目成果

Kazuya Kato: "Bloch's conductor formula"Proc. Jangjeon Math. Soc. 1. 1. 91-95 (2000)

加藤和也：“布洛赫的指挥公式”Proc。

Kazuya Kato, Sampei Usui: "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math. (to appear).

Kazuya Kato、Sampei Usui：“Borel-Serre 空间和 SL(2) 轨道空间”纯数学高级研究。

Kazuya Kato, Toshiharu Matsubara, Chikara Nakayama: "Log C^∞ functions and degencvation of Hodge structures"Advanced Studies in Pure Math. (発表予定).

Kazuya Kato、Toshiharu Matsubara、Chikara Nakayama：“Log C^∞ 函数和 Hodge 结构的退化”纯数学高级研究（待提交）。

Kazuya Kato,Chikara Nakayama: "Log Betti cohomology,log etale cohomology,and log de Rham cohomology of log Schemes over C"Kodai Math.J. 22. 161-186 (1999)

Kazuya Kato、Chikara Nakayama：“C 上的对数方案的 Log Betti 上同调、log etale 上同调和 log de Rham 上同调”Kodai Math.J。

Kazuya Kato: "Euler systems, Iwasawa theory and Selmer groups"Kodai Math J.. 22. 313-372 (1999)

加藤和也：“欧拉系统、岩泽理论和塞尔默群”Kodai Math J.. 22. 313-372 (1999)