Study of relations and applications of Arithmetic Geometry to branches of Algebra

算术几何与代数分支的关系及应用研究

• 批准号: 12440001
• 负责人: MORITA Yasuo
• 金额: $ 9.73万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440001/
• 关键词: Number Theory; Algebraic Geometry; Ring Theory; Group Theory; Representation Theory; 数論的幾何学; 代数学; 整数論; 代数幾何学; 解析数論

In this research, we have studied relations and applications of Arithmetic Geometry to branches of Algebra. In each year, we have organized an Algebra Symposium which covers all branches of Algebra, a symposium specialized in Ring Theory, and a symposium specialized in Analytic Number Theory. We have organized a symposium specialized in Algebraic Geometry in 2003. We have made a list of research mathematicians working on Algebra also.

本文研究了算术几何与代数分支的关系及其应用。在每一年，我们都组织了一个代数研讨会，其中涵盖了代数的所有分支，一个专题研讨会专门在环理论，和一个专题研讨会专门在解析数论。我们在2003年组织了一次代数几何专题讨论会。我们已经做了一个列表的研究数学家工作代数也。

项目成果

N.Hara, K.Watanabe: "F-regular and F-pure Rings vs. Log-terminal and Log-canonical Singularities"Journal Algebraic Geometry. 11. 363-392 (2002)

N.Hara、K.Watanabe：“F-正则环和 F-纯环与对数末端和对数规范奇点”期刊代数几何。

Ahmed Abbes, T.Saito: "Ramification of local fields with imperfect residue fields"Americal J.of Mathematics. 124.5. 879-920 (2002)

艾哈迈德·阿贝斯 (Ahmed Abbes)、T.Saito：“具有不完美残差场的局部场的分支”美国数学杂志。

G. van der Geer, T. Katura: "An invariant for varieties in positive characteristic"Contemporary Math. 300, in Alg. Number Theory and Alg. Geometry. 131-141 (2002)

G. van der Geer，T. Katura：“积极特征中品种的不变量”当代数学。

E.Bannai and M.Koike: "Some results on modular forms-subgroups of the modular group whose ring of modular forms is a polynomial ring"to appear in Advanced Studies in Pure Mathematics. (2001)

E.Bannai 和 M.Koike：“关于模形式的一些结果 - 模群的子群，其模形式的环是多项式环”出现在《纯数学高级研究》中。

K.Watanabe and K.Yoshida: "Hilbert-Kunz multiplicity and an inequality between multiplicity and colength"Journal of Algebra. 230. 295-317 (2000)

K.Watanabe 和 K.Yoshida：“Hilbert-Kunz 重数以及重数与 colength 之间的不等式”代数杂志。