二变量等变Iwasawa理论的拟合理想及其在CM椭圆曲线上的应用

IF 0.4 4区数学 Q4 MATHEMATICS

Tokyo Journal of Mathematics Pub Date : 2020-08-07 DOI:10.3836/tjm/1502179347

T. Kataoka

{"title":"二变量等变Iwasawa理论的拟合理想及其在CM椭圆曲线上的应用","authors":"T. Kataoka","doi":"10.3836/tjm/1502179347","DOIUrl":null,"url":null,"abstract":"We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide an application to Selmer groups of elliptic curves with complex multiplication.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Fitting Ideals in Two-variable Equivariant Iwasawa Theory and an Application to CM Elliptic Curves\",\"authors\":\"T. Kataoka\",\"doi\":\"10.3836/tjm/1502179347\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide an application to Selmer groups of elliptic curves with complex multiplication.\",\"PeriodicalId\":48976,\"journal\":{\"name\":\"Tokyo Journal of Mathematics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tokyo Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3836/tjm/1502179347\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tokyo Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3836/tjm/1502179347","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

研究了虚二次域的二变量阿贝尔扩展的等变Iwasawa理论。本文的主要目标之一是使用$p$- $L$-函数描述Iwasawa模块的拟合理想。给出了椭圆曲线复数乘法的Selmer群的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Fitting Ideals in Two-variable Equivariant Iwasawa Theory and an Application to CM Elliptic Curves

We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide an application to Selmer groups of elliptic curves with complex multiplication.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Tokyo Journal of Mathematics MATHEMATICS-

CiteScore

0.70

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Tokyo Journal of Mathematics was founded in 1978 with the financial support of six institutions in the Tokyo area: Gakushuin University, Keio University, Sophia University, Tokyo Metropolitan University, Tsuda College, and Waseda University. In 2000 Chuo University and Meiji University, in 2005 Tokai University, and in 2013 Tokyo University of Science, joined as supporting institutions.