{"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}
引用次数: 0
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.