{"title":"阿贝尔变换上零环的高Chow群上的滤除","authors":"Buntaro Kakinoki","doi":"10.2748/tmj.20191030","DOIUrl":null,"url":null,"abstract":"In this paper we extend Gazaki's results on the Chow groups of abelian varieties to the higher Chow groups. We introduce a Gazaki type filtration on the higher Chow group of zero-cycles on an abelian variety, whose graded quotients are connected to the Somekawa type $K$-group. Via the \\'{e}tale cycle map, we will compare this filtration with a filtration on the \\'{e}tale cohomology induced by the Hochschild-Serre spectral sequence. As an application over local fields, we obtain an estimate of the kernel of the reciprocity map.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2019-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A filtration on the higher Chow group of zero cycles on an abelian variety\",\"authors\":\"Buntaro Kakinoki\",\"doi\":\"10.2748/tmj.20191030\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we extend Gazaki's results on the Chow groups of abelian varieties to the higher Chow groups. We introduce a Gazaki type filtration on the higher Chow group of zero-cycles on an abelian variety, whose graded quotients are connected to the Somekawa type $K$-group. Via the \\\\'{e}tale cycle map, we will compare this filtration with a filtration on the \\\\'{e}tale cohomology induced by the Hochschild-Serre spectral sequence. As an application over local fields, we obtain an estimate of the kernel of the reciprocity map.\",\"PeriodicalId\":54427,\"journal\":{\"name\":\"Tohoku Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-01-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tohoku Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2748/tmj.20191030\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tohoku Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2748/tmj.20191030","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A filtration on the higher Chow group of zero cycles on an abelian variety
In this paper we extend Gazaki's results on the Chow groups of abelian varieties to the higher Chow groups. We introduce a Gazaki type filtration on the higher Chow group of zero-cycles on an abelian variety, whose graded quotients are connected to the Somekawa type $K$-group. Via the \'{e}tale cycle map, we will compare this filtration with a filtration on the \'{e}tale cohomology induced by the Hochschild-Serre spectral sequence. As an application over local fields, we obtain an estimate of the kernel of the reciprocity map.