Comptes Rendus
no. 5
Algebraic geometry
On the Chow ring of certain rational cohomology tori

Presented by: Claire Voisin

Zhi Jiang1, 2; Qizheng Yin3
1 Département de mathématiques, CNRS UMR 8628, Université Paris-Sud, Bâtiment 425, 91405 Orsay cedex, France
2 Shanghai Center for Mathematical Sciences, Fudan University, No. 220 Handan Road, Yangpu District, Shanghai 200433, China
3 Beijing International Center for Mathematical Research, Peking University, No. 5 Yiheyuan Road, Haidian District Beijing 100871, China
Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 571-576.

Let f:X→A be an abelian cover from a complex algebraic variety with quotient singularities to an abelian variety. We show that f⁎ induces an isomorphism between the rational cohomology rings H•(A,Q) and H•(X,Q) if and only if f⁎ induces an isomorphism between the Chow rings with rational coefficients CH•(A)Q and CH•(X)Q.

Soit f:X→A un revêtement abélien d'une variété algébrique complexe à singularités-quotient dans une variété abélienne. Nous montrons que f⁎ induit un isomorphisme entre les anneaux de cohomologie rationnelle H•(A,Q) et H•(X,Q) si et seulement si f⁎ induit un isomorphisme entre les anneaux de Chow à coefficients rationnels CH•(A)Q et CH•(X)Q.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.04.006

Zhi Jiang 1, 2; Qizheng Yin 3

1 Département de mathématiques, CNRS UMR 8628, Université Paris-Sud, Bâtiment 425, 91405 Orsay cedex, France
2 Shanghai Center for Mathematical Sciences, Fudan University, No. 220 Handan Road, Yangpu District, Shanghai 200433, China
3 Beijing International Center for Mathematical Research, Peking University, No. 5 Yiheyuan Road, Haidian District Beijing 100871, China 
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Zhi Jiang; Qizheng Yin. On the Chow ring of certain rational cohomology tori. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 571-576. doi : 10.1016/j.crma.2017.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.006/

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