加藤对惰性素数上反旋转 CM 变形的ε猜想

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-08-10 DOI:10.1016/j.jnt.2024.06.014

Ashay A. Burungale, Shinichi Kobayashi, Kazuto Ota, Seidai Yasuda

{"title":"加藤对惰性素数上反旋转 CM 变形的ε猜想","authors":"Ashay A. Burungale, Shinichi Kobayashi, Kazuto Ota, Seidai Yasuda","doi":"10.1016/j.jnt.2024.06.014","DOIUrl":null,"url":null,"abstract":"We present an explicit construction of Kato's local epsilon isomorphism for the anticyclotomic deformation of a Lubin-Tate formal group of height two by using Rubin's theory on local units in the anticyclotomic tower. We also prove Kato's global epsilon conjecture for the anticyclotomic deformation of a CM elliptic curve at an inert prime.","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"17 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kato's epsilon conjecture for anticyclotomic CM deformations at inert primes\",\"authors\":\"Ashay A. Burungale, Shinichi Kobayashi, Kazuto Ota, Seidai Yasuda\",\"doi\":\"10.1016/j.jnt.2024.06.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an explicit construction of Kato's local epsilon isomorphism for the anticyclotomic deformation of a Lubin-Tate formal group of height two by using Rubin's theory on local units in the anticyclotomic tower. We also prove Kato's global epsilon conjecture for the anticyclotomic deformation of a CM elliptic curve at an inert prime.\",\"PeriodicalId\":50110,\"journal\":{\"name\":\"Journal of Number Theory\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.jnt.2024.06.014\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.jnt.2024.06.014","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们利用鲁宾关于反循环塔中局部单元的理论，为高度为二的卢宾-塔特形式群的反循环变形提出了加藤局部ε同构的明确构造。我们还证明了加藤关于 CM 椭圆曲线在惰性素数处反循环变形的全局ε猜想。

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

Kato's epsilon conjecture for anticyclotomic CM deformations at inert primes

We present an explicit construction of Kato's local epsilon isomorphism for the anticyclotomic deformation of a Lubin-Tate formal group of height two by using Rubin's theory on local units in the anticyclotomic tower. We also prove Kato's global epsilon conjecture for the anticyclotomic deformation of a CM elliptic curve at an inert prime.

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

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.