{"title":"塔特上同调","authors":"Tate Cohomology, Dino Zavattini","doi":"10.1090/surv/262/07","DOIUrl":null,"url":null,"abstract":". Tate cohomology is a useful synthesis of group homology and cohomology. It has applications in class field theory—in particular in proving the Artin reciprocity—as well as in the study of Tate spectra. In this paper we provide three equivalent definitions of Tate cohomology and define the cup product on it.","PeriodicalId":121714,"journal":{"name":"Maximal Cohen–Macaulay Modules and Tate Cohomology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Tate cohomology\",\"authors\":\"Tate Cohomology, Dino Zavattini\",\"doi\":\"10.1090/surv/262/07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Tate cohomology is a useful synthesis of group homology and cohomology. It has applications in class field theory—in particular in proving the Artin reciprocity—as well as in the study of Tate spectra. In this paper we provide three equivalent definitions of Tate cohomology and define the cup product on it.\",\"PeriodicalId\":121714,\"journal\":{\"name\":\"Maximal Cohen–Macaulay Modules and Tate Cohomology\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Maximal Cohen–Macaulay Modules and Tate Cohomology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/surv/262/07\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Maximal Cohen–Macaulay Modules and Tate Cohomology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/surv/262/07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. Tate cohomology is a useful synthesis of group homology and cohomology. It has applications in class field theory—in particular in proving the Artin reciprocity—as well as in the study of Tate spectra. In this paper we provide three equivalent definitions of Tate cohomology and define the cup product on it.
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