{"title":"Brauer-Manin阻塞","authors":"Yeqin Liu Uic","doi":"10.1090/mmono/246/11","DOIUrl":null,"url":null,"abstract":": The Brauer-Manin obstruction is a refinement of the Hasse principle, which gives a sufficient condition for non-existence of rational points on an algebraic variety. In this talk I will introduce the Brauer group of an algebraic variety and explain the Brauer-Manin obstruction geometrically. Then we will see through an example that the Brauer-Manin obstruction is a strict refinement of the Hasse principle.","PeriodicalId":371565,"journal":{"name":"Translations of Mathematical\n Monographs","volume":"106 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Brauer-Manin Obstruction\",\"authors\":\"Yeqin Liu Uic\",\"doi\":\"10.1090/mmono/246/11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": The Brauer-Manin obstruction is a refinement of the Hasse principle, which gives a sufficient condition for non-existence of rational points on an algebraic variety. In this talk I will introduce the Brauer group of an algebraic variety and explain the Brauer-Manin obstruction geometrically. Then we will see through an example that the Brauer-Manin obstruction is a strict refinement of the Hasse principle.\",\"PeriodicalId\":371565,\"journal\":{\"name\":\"Translations of Mathematical\\n Monographs\",\"volume\":\"106 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Translations of Mathematical\\n Monographs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mmono/246/11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Translations of Mathematical\n Monographs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mmono/246/11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
: The Brauer-Manin obstruction is a refinement of the Hasse principle, which gives a sufficient condition for non-existence of rational points on an algebraic variety. In this talk I will introduce the Brauer group of an algebraic variety and explain the Brauer-Manin obstruction geometrically. Then we will see through an example that the Brauer-Manin obstruction is a strict refinement of the Hasse principle.
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