Arithmetic of Z_p-field and geometry of algebraic curves

本项目的目的是通过ZP-域的概念来研究代数数域上的岩泽理论，并将其与椭圆曲线的算术理论进行比较。本课题所获得的结果涉及(1)岩泽理论的基本构造；(2)代数数域上的椭圆曲线的算法，并将其收录在本课题的成果中。在本课题中，还进行了以下活动：(3)Kummer研究组的活动；(4)利用计算机代数系统进行实例计算。(3)阅读Kummer的数论论文，希望在经典的伟大著作中找到新的想法。(4)是利用近年来广泛进步的计算机能力为岩泽理论寻找好例子的尝试。对于(3)和(4)，还没有具体的结果公布。但我们希望在未来以某种形式公布作为该项目一部分开始的活动(3)和(4)的结果。

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.