{"title":"局部和全局域上连通约化群上的Tate-Shafarevich核、弱Brauer和r等价","authors":"N. Q. Thang","doi":"10.2422/2036-2145.201703_004","DOIUrl":null,"url":null,"abstract":"We introduce a new equivalence relation on k-points of connected reductive groups over an arbitrary field, which coincides with the usual Brauer equivalence when the characteristic is 0, and study its relation with R-equivalence relation and other basic arithmetic-geometric invariants of the given group over local and global fields of any characteristic via some local-global exact sequences. Mathematics Subject Classification (2010): 11E72 (primary); 20G10, 20G30, 20G35 (secondary).","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"22 1","pages":"1"},"PeriodicalIF":1.2000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Tate-Shafarevich kernel, weak Brauer and R-equivalence on connected reductive groups over local and global fields\",\"authors\":\"N. Q. Thang\",\"doi\":\"10.2422/2036-2145.201703_004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a new equivalence relation on k-points of connected reductive groups over an arbitrary field, which coincides with the usual Brauer equivalence when the characteristic is 0, and study its relation with R-equivalence relation and other basic arithmetic-geometric invariants of the given group over local and global fields of any characteristic via some local-global exact sequences. Mathematics Subject Classification (2010): 11E72 (primary); 20G10, 20G30, 20G35 (secondary).\",\"PeriodicalId\":50966,\"journal\":{\"name\":\"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze\",\"volume\":\"22 1\",\"pages\":\"1\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2422/2036-2145.201703_004\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2422/2036-2145.201703_004","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Tate-Shafarevich kernel, weak Brauer and R-equivalence on connected reductive groups over local and global fields
We introduce a new equivalence relation on k-points of connected reductive groups over an arbitrary field, which coincides with the usual Brauer equivalence when the characteristic is 0, and study its relation with R-equivalence relation and other basic arithmetic-geometric invariants of the given group over local and global fields of any characteristic via some local-global exact sequences. Mathematics Subject Classification (2010): 11E72 (primary); 20G10, 20G30, 20G35 (secondary).
期刊介绍：
The Annals of the Normale Superiore di Pisa, Science Class, publishes papers that contribute to the development of Mathematics both from the theoretical and the applied point of view. Research papers or papers of expository type are considered for publication.
The Annals of the Normale Scuola di Pisa - Science Class is published quarterly
Soft cover, 17x24
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