{"title":"When Is a Reductive Group Scheme Linear?","authors":"P. Gille","doi":"10.1307/mmj/20217208","DOIUrl":null,"url":null,"abstract":"We show that a reductive group scheme over a base scheme S admits a faithful linear representation if and only if its radical torus is isotrivial, that is, it splits after a finite {\\'e}tale cover.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1307/mmj/20217208","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
We show that a reductive group scheme over a base scheme S admits a faithful linear representation if and only if its radical torus is isotrivial, that is, it splits after a finite {\'e}tale cover.
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