{"title":"The Generalized Hodge and Bloch Conjectures are Equivalent for General Complete Intersections, II","authors":"C. Voisin","doi":"10.24033/ASENS.2193","DOIUrl":null,"url":null,"abstract":"We prove an unconditional (but slightly weakened) version of the main result of (13), which was, starting from dimension 4, conditional to the Lefschetz standard conjecture. Let X be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on CH(X)Q). We prove that if the cohomology of a general hypersurface Y in X is \"parameterized by cycles of dimension c\", then the Chow groups CHi(Y )Q are trivial for i ≤ c − 1.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"34 1","pages":"449-475"},"PeriodicalIF":1.3000,"publicationDate":"2011-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"68","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ASENS.2193","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 68
Abstract
We prove an unconditional (but slightly weakened) version of the main result of (13), which was, starting from dimension 4, conditional to the Lefschetz standard conjecture. Let X be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on CH(X)Q). We prove that if the cohomology of a general hypersurface Y in X is "parameterized by cycles of dimension c", then the Chow groups CHi(Y )Q are trivial for i ≤ c − 1.
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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