Arithmetic of Z_p-field and geometry of algebraic curves

Z_p场的算术和代数曲线的几何

• 批准号: 09640008
• 负责人: NAKAJIMA Shoichi
• 金额: $ 1.92万
• 依托单位: Gakushuin University (1998)The University of Tokyo (1997)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640008/
• 关键词: Iwasawa theory; Algebraic number field

The aim of this project was investigating Iwasawa theory of algebraic number fields through the notion of Zp-field, and through comparing it with the arithmetic theory of elliptic curves.The results obtained in the project are concerned with(1) basic construction of Iwasawa theory(2) arithmetic of elliptic curves over algebraic number fields, and they are collected in the publication of the results of this project.In this project the following activities were also proceeded :(3) activity of "Kummer Research Group"(4) computation of examples by using computer algebra system.(3) is a project for reading papers of Kummer on number theory, expecting to find new ideas in classical great works.(4) is an attempt to find good examples for Iwasawa theory by making use of computers whose ability is extensively advanced recently.For (3) and (4) no concrete results have been published yet.However, in future we expect to publish, in some form, the results of activities (3) and (4) that were begun as part of this project.

The aim of this project was investigating Iwasawa theory of algebraic number fields through the notion of Zp-field, and through comparing it with the arithmetic theory of elliptic curves.The results obtained in the project are concerned with(1) basic construction of Iwasawa theory(2) arithmetic of elliptic curves over algebraic number fields, and they are collected in the publication of the results of this project.In this project the following还进行了活动：（3）“ Kummer Research Group”（4）使用计算机代数系统计算示例的活动。（3）是一个阅读Kummer关于数字理论的论文的项目，期望在古典伟大作品中找到新的想法。（4）试图通过在iWasawa Theopers进行良好的示例来使用iWasawa Theemens来使用iWasawa Theopers的范围，而否则尚无广泛的计算机，并且在最近的计算机上进行了广泛的表现。然而，无论将来，我们希望以某种形式发布作为该项目的一部分开始的活动（3）和（4）的结果。

项目成果

H.Ichimura, H.Sumida: "On the Iwasawa invariants of certain real abeliau fields" Tohoku Math. J.49. 203-215 (1997)

H.Ich​​imura、H.Sumida：“论某些真实阿贝廖域的岩泽不变量”东北数学。

中島匠一: "岩沢理論入門" 数理解析研究所講究録. 1026. 28-42 (1998)

Takuichi Nakajima：“岩泽理论导论”数学分析研究所的 Kokyuroku。1026. 28-42 (1998)。

H.Ichimura: "Local units modulo Gauss sums" J.Number Theory. 68. 36-56 (1998)

H.Ich​​imura：“局部单位模高斯和”J.数论。

H.Ichimura: "Class numbers of real quadratic function fields of genus one" Finite Fields and Their Applications. 3. 181-185 (1997)

H.Ich​​imura：“属一实二次函数域的类数”有限域及其应用。

S.Nakajima: "Introduction to Iwasawa theory (in Japanese)" RIMS Kokyu-roku. 1026. 28-42 (1998)

S.Nakajima：“岩泽理论简介（日语）”RIMS Kokyu-roku。