{"title":"通过推导出森田不变性、局部化和A(1)-同伦不变性的基本定理","authors":"Gonçalo Tabuada","doi":"10.1017/IS011004009JKT155","DOIUrl":null,"url":null,"abstract":"We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"407-420"},"PeriodicalIF":0.0000,"publicationDate":"2011-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011004009JKT155","citationCount":"18","resultStr":"{\"title\":\"The fundamental theorem via derived Morita invariance, localization, and A(1)-homotopy invariance\",\"authors\":\"Gonçalo Tabuada\",\"doi\":\"10.1017/IS011004009JKT155\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"9 1\",\"pages\":\"407-420\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS011004009JKT155\",\"citationCount\":\"18\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS011004009JKT155\",\"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/IS011004009JKT155","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The fundamental theorem via derived Morita invariance, localization, and A(1)-homotopy invariance
We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively.
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