{"title":"THE DIAGONAL CYCLE EULER SYSTEM FOR","authors":"Raúl Alonso, Francesc Castella, Óscar Rivero","doi":"10.1017/s1474748023000221","DOIUrl":null,"url":null,"abstract":"\n We construct an anticyclotomic Euler system for the Rankin–Selberg convolutions of two modular forms, using p-adic families of generalised Gross–Kudla–Schoen diagonal cycles. As applications of this construction, we prove new results on the Bloch–Kato conjecture in analytic ranks zero and one, and a divisibility towards an Iwasawa main conjecture.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1474748023000221","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct an anticyclotomic Euler system for the Rankin–Selberg convolutions of two modular forms, using p-adic families of generalised Gross–Kudla–Schoen diagonal cycles. As applications of this construction, we prove new results on the Bloch–Kato conjecture in analytic ranks zero and one, and a divisibility towards an Iwasawa main conjecture.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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