{"title":"Milnor k理论中带系数零环的约束同构","authors":"Morten Lüders","doi":"10.4310/CJM.2019.V7.N1.A1","DOIUrl":null,"url":null,"abstract":"We prove a restriction isomorphism for zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore we relate zero-cycles with coefficients in Milnor K-theory to \\'etale cohomology and certain Kato complexes and deduce finiteness results for zero-cycles with coefficients in Milnor K-theory over local fields.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2017-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A restriction isomorphism for zero-cycles with coefficients in Milnor K-theory\",\"authors\":\"Morten Lüders\",\"doi\":\"10.4310/CJM.2019.V7.N1.A1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a restriction isomorphism for zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore we relate zero-cycles with coefficients in Milnor K-theory to \\\\'etale cohomology and certain Kato complexes and deduce finiteness results for zero-cycles with coefficients in Milnor K-theory over local fields.\",\"PeriodicalId\":48573,\"journal\":{\"name\":\"Cambridge Journal of Mathematics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2017-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cambridge Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/CJM.2019.V7.N1.A1\",\"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":"Cambridge Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/CJM.2019.V7.N1.A1","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A restriction isomorphism for zero-cycles with coefficients in Milnor K-theory
We prove a restriction isomorphism for zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore we relate zero-cycles with coefficients in Milnor K-theory to \'etale cohomology and certain Kato complexes and deduce finiteness results for zero-cycles with coefficients in Milnor K-theory over local fields.
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