{"title":"An integral model of the perfectoid modular curve","authors":"Juan Esteban Rodr'iguez Camargo","doi":"10.5802/JEP.170","DOIUrl":null,"url":null,"abstract":"We construct a formal integral model of the perfectoid modular curve. Studying this object, we provide some vanishing results in the coherent cohomology at perfectoid level. We also relate the completed cohomology of the modular tower with the integral cusp forms of weight $2$.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"132 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de l’École polytechnique — Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/JEP.170","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a formal integral model of the perfectoid modular curve. Studying this object, we provide some vanishing results in the coherent cohomology at perfectoid level. We also relate the completed cohomology of the modular tower with the integral cusp forms of weight $2$.
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