{"title":"Milnor k理论上范数映射的连续性","authors":"M. Morrow","doi":"10.1017/IS011011005JKT166","DOIUrl":null,"url":null,"abstract":"The norm map on the Milnor K-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"10 1","pages":"565-577"},"PeriodicalIF":0.0000,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011011005JKT166","citationCount":"4","resultStr":"{\"title\":\"Continuity of the norm map on Milnor K-theory\",\"authors\":\"M. Morrow\",\"doi\":\"10.1017/IS011011005JKT166\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The norm map on the Milnor K-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"10 1\",\"pages\":\"565-577\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS011011005JKT166\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS011011005JKT166\",\"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/IS011011005JKT166","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The norm map on the Milnor K-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.
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