{"title":"除法代数中单位群的动机","authors":"E. Shinder","doi":"10.1017/IS014003007JKT258","DOIUrl":null,"url":null,"abstract":"We consider the algebraic group GL1(A), where A is a division algebra of prime degree over a eld F , and the associated motive in the Voevodsky category of motivic complexes DM eff (F ). We relate the motive of GL1(A) to the motive of the Cech simplicial scheme X , associated to the Severi-Brauer variety of A, and compute the second dierential in the resulting spectral sequence for motivic cohomology.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"13 1","pages":"533-561"},"PeriodicalIF":0.0000,"publicationDate":"2014-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS014003007JKT258","citationCount":"5","resultStr":"{\"title\":\"On the motive of the group of units of a division algebra\",\"authors\":\"E. Shinder\",\"doi\":\"10.1017/IS014003007JKT258\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the algebraic group GL1(A), where A is a division algebra of prime degree over a eld F , and the associated motive in the Voevodsky category of motivic complexes DM eff (F ). We relate the motive of GL1(A) to the motive of the Cech simplicial scheme X , associated to the Severi-Brauer variety of A, and compute the second dierential in the resulting spectral sequence for motivic cohomology.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"13 1\",\"pages\":\"533-561\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS014003007JKT258\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS014003007JKT258\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS014003007JKT258","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the motive of the group of units of a division algebra
We consider the algebraic group GL1(A), where A is a division algebra of prime degree over a eld F , and the associated motive in the Voevodsky category of motivic complexes DM eff (F ). We relate the motive of GL1(A) to the motive of the Cech simplicial scheme X , associated to the Severi-Brauer variety of A, and compute the second dierential in the resulting spectral sequence for motivic cohomology.
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