Soit un revêtement abélien d'une variété algébrique complexe à singularités-quotient dans une variété abélienne. Nous montrons que induit un isomorphisme entre les anneaux de cohomologie rationnelle et si et seulement si induit un isomorphisme entre les anneaux de Chow à coefficients rationnels et .
Let be an abelian cover from a complex algebraic variety with quotient singularities to an abelian variety. We show that induces an isomorphism between the rational cohomology rings and if and only if induces an isomorphism between the Chow rings with rational coefficients and .
Accepté le :
Publié le :
Zhi Jiang 1, 2 ; Qizheng Yin 3
@article{CRMATH_2017__355_5_571_0, author = {Zhi Jiang and Qizheng Yin}, title = {On the {Chow} ring of certain rational cohomology tori}, journal = {Comptes Rendus. Math\'ematique}, pages = {571--576}, publisher = {Elsevier}, volume = {355}, number = {5}, year = {2017}, doi = {10.1016/j.crma.2017.04.006}, language = {en}, }
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/
[1] Sur l'anneau de Chow d'une variété abélienne, Math. Ann., Volume 273 (1986) no. 4, pp. 647-651
[2] Complex Abelian Varieties, Grundlehren der Mathematischen Wissenschaften, vol. 302, Springer-Verlag, Berlin, 2004
[3] Rational cohomology tori, Geom. Topol., Volume 21 (2017) no. 2, pp. 1095-1130
[4] Smooth toric Deligne–Mumford stacks, J. Reine Angew. Math., Volume 648 (2010), pp. 201-244
[5] Characterization of abelian varieties, Compos. Math., Volume 43 (1981) no. 2, pp. 253-276
[6] Abelian covers of algebraic varieties, J. Reine Angew. Math., Volume 417 (1991), pp. 191-213
[7] Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math., Volume 97 (1989) no. 3, pp. 613-670
Cité par Sources :
Commentaires - Politique