{"title":"关于大图伽罗瓦表示法的注解","authors":"N. M. Katz","doi":"10.4171/lem/65-3/4-1","DOIUrl":null,"url":null,"abstract":"Given an integer N ≥ 3, we will first construct reasonably “motivic” representations ρ : Gal(Q/Q(ζN ))→ GL(n,Q`) with open image, for any ` which is 1 mod N and for certain n. We will do this in three different ways. The third of them has a descent to Q when N is 3 or 4. This provides us with motivic galois representations of Gal(Q/Q) with open image in GL(n,Q`) for any even n ≥ 6 and any ` which is ≡ 1 mod 3 or mod 4.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A note on Galois representations with big image\",\"authors\":\"N. M. Katz\",\"doi\":\"10.4171/lem/65-3/4-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given an integer N ≥ 3, we will first construct reasonably “motivic” representations ρ : Gal(Q/Q(ζN ))→ GL(n,Q`) with open image, for any ` which is 1 mod N and for certain n. We will do this in three different ways. The third of them has a descent to Q when N is 3 or 4. This provides us with motivic galois representations of Gal(Q/Q) with open image in GL(n,Q`) for any even n ≥ 6 and any ` which is ≡ 1 mod 3 or mod 4.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/lem/65-3/4-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"L’Enseignement Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/lem/65-3/4-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
摘要
给定整数N≥3，我们将首先构建合理的“动机”表示ρ: Gal(Q/Q(ζN))→GL(N,Q ')与开放图像，对于任意'为1 mod N和确定N。我们将以三种不同的方式完成此操作。当N等于3或4时，第三个会下降到Q。这为我们提供了GL(n,Q ')中任意偶数n≥6和任意'≡1 mod 3或mod 4的开象Gal(Q/Q)的动机伽罗式表示。
Given an integer N ≥ 3, we will first construct reasonably “motivic” representations ρ : Gal(Q/Q(ζN ))→ GL(n,Q`) with open image, for any ` which is 1 mod N and for certain n. We will do this in three different ways. The third of them has a descent to Q when N is 3 or 4. This provides us with motivic galois representations of Gal(Q/Q) with open image in GL(n,Q`) for any even n ≥ 6 and any ` which is ≡ 1 mod 3 or mod 4.
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