广义Hodge猜想与Bloch猜想对于一般完全交是等价的，2

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2011-07-13 DOI:10.24033/ASENS.2193

C. Voisin

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引用次数: 68

摘要

我们证明了(13)的主要结果的一个无条件(但稍微弱化)版本，从第4维开始，它是Lefschetz标准猜想的条件。设X是具有平凡Chow群的一个变种，即到上同调的循环类映射在CH(X)Q上是内射的。证明了如果X中的一般超曲面Y的上同调“被c维环参数化”，则对于i≤c−1,Chow群CHi(Y)Q是平凡的。

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The Generalized Hodge and Bloch Conjectures are Equivalent for General Complete Intersections, II

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.

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

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.