Arithmetic of Z_p-field and geometry of algebraic curves

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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.