{"title":"约化群方案何时是线性的?","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":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"67 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"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\":49820,\"journal\":{\"name\":\"Michigan Mathematical Journal\",\"volume\":\"67 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Michigan Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1307/mmj/20217208\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Michigan Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1307/mmj/20217208","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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The Michigan Mathematical Journal is available electronically through the Project Euclid web site. The electronic version is available free to all paid subscribers. The Journal must receive from institutional subscribers a list of Internet Protocol Addresses in order for members of their institutions to have access to the online version of the Journal.
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