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.

该项目的目的是通过 Zp 场的概念研究 Iwasawa 代数数域理论，并将其与椭圆曲线的算术理论进行比较。该项目获得的结果涉及（1）Iwasawa 理论的基本构造（2）代数数域上的椭圆曲线的算术，并将它们收集在本项目成果的出版物中。在本项目中还进行了以下活动：（3）“Kummer”活动研究小组”(4)使用计算机代数系统计算例子。(3)是阅读Kummer数论论文的项目，期望在经典伟大著作中找到新的想法。(4)是寻找好的例子的尝试利用最近能力得到广泛提高的计算机来研究岩泽理论。对于（3）和（4），尚未公布具体结果。但是，将来我们期望以某种形式公布活动结果（3） ）和（4）作为一部分开始这个项目的。

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: "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。

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。

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。