加藤对惰性素数上反旋转 CM 变形的ε猜想

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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.jnt.2024.06.014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.jnt.2024.06.014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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

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