{"title":"Sharifi猜想中的层次兼容性","authors":"E. Lecouturier, Jun Wang","doi":"10.4153/s0008439523000267","DOIUrl":null,"url":null,"abstract":"Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(\\mathbf{Z}[\\zeta_M, \\frac{1}{M}])$, where $\\zeta_M$ is a primitive $M$th root of unity. We study how these maps relate when $M$ varies. Our method relies on the techniques developed by Sharifi and Venkatesh.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Level compatibility in Sharifi’s conjecture\",\"authors\":\"E. Lecouturier, Jun Wang\",\"doi\":\"10.4153/s0008439523000267\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(\\\\mathbf{Z}[\\\\zeta_M, \\\\frac{1}{M}])$, where $\\\\zeta_M$ is a primitive $M$th root of unity. We study how these maps relate when $M$ varies. Our method relies on the techniques developed by Sharifi and Venkatesh.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008439523000267\",\"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/10.4153/s0008439523000267","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(\mathbf{Z}[\zeta_M, \frac{1}{M}])$, where $\zeta_M$ is a primitive $M$th root of unity. We study how these maps relate when $M$ varies. Our method relies on the techniques developed by Sharifi and Venkatesh.
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