{"title":"On the Mazur-Tate conjecture for prime conductor and Mazur's Eisenstein ideal","authors":"Emmanuel Lecouturier","doi":"10.1353/ajm.2023.a907701","DOIUrl":null,"url":null,"abstract":"abstract: In 1995, Ehud de Shalit proved an analogue of a conjecture of Mazur-Tate for the modular Jacobian $J_0(p)$. His main result was valid away from the Eisenstein primes. We complete the work of de Shalit by including the Eisenstein primes, and give some applications such as an elementary combinatorial identity involving discrete logarithms of difference of supersingular $j$-invariants. An important tool is our recent work on the so called ``generalized cuspidal $1$-motive''.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"89 1","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1353/ajm.2023.a907701","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
abstract: In 1995, Ehud de Shalit proved an analogue of a conjecture of Mazur-Tate for the modular Jacobian $J_0(p)$. His main result was valid away from the Eisenstein primes. We complete the work of de Shalit by including the Eisenstein primes, and give some applications such as an elementary combinatorial identity involving discrete logarithms of difference of supersingular $j$-invariants. An important tool is our recent work on the so called ``generalized cuspidal $1$-motive''.
1995年，Ehud de Shalit证明了模雅可比矩阵$J_0(p)$的Mazur-Tate猜想的一个类似。他的主要结果在不考虑爱森斯坦素数的情况下是有效的。我们通过引入爱森斯坦素数完成了de Shalit的工作，并给出了一些应用，如涉及超奇异$j$不变量差分离散对数的初等组合恒等式。一个重要的工具是我们最近关于所谓的“广义逆$1$动机”的研究。
期刊介绍：
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
