{"title":"A remark on the Tate Conjecture","authors":"B. Moonen","doi":"10.1090/JAG/720","DOIUrl":null,"url":null,"abstract":"The strong version of the Tate conjecture has two parts: an assertion (S) about semisimplicity of Galois representations and an assertion (T) which says that every Tate class is algebraic. We show that in characteristic \n\n \n 0\n 0\n \n\n, (T) implies (S). In characteristic \n\n \n p\n p\n \n\n an analogous result is true under stronger assumptions.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2017-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/720","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/JAG/720","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 18
Abstract
The strong version of the Tate conjecture has two parts: an assertion (S) about semisimplicity of Galois representations and an assertion (T) which says that every Tate class is algebraic. We show that in characteristic
0
0
, (T) implies (S). In characteristic
p
p
an analogous result is true under stronger assumptions.
期刊介绍：
The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology.
This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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