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 .
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@article{CRMATH_2017__355_5_571_0, author = {Jiang, Zhi and Yin, Qizheng}, 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}, url = {http://www.numdam.org/articles/10.1016/j.crma.2017.04.006/} }
TY - JOUR AU - Jiang, Zhi AU - Yin, Qizheng TI - On the Chow ring of certain rational cohomology tori JO - Comptes Rendus. Mathématique PY - 2017 SP - 571 EP - 576 VL - 355 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.04.006/ DO - 10.1016/j.crma.2017.04.006 LA - en ID - CRMATH_2017__355_5_571_0 ER -
%0 Journal Article %A Jiang, Zhi %A Yin, Qizheng %T On the Chow ring of certain rational cohomology tori %J Comptes Rendus. Mathématique %D 2017 %P 571-576 %V 355 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.04.006/ %R 10.1016/j.crma.2017.04.006 %G en %F CRMATH_2017__355_5_571_0
Jiang, Zhi; Yin, Qizheng. On the Chow ring of certain rational cohomology tori. Comptes Rendus. Mathématique, Tome 355 (2017) no. 5, pp. 571-576. doi : 10.1016/j.crma.2017.04.006. http://www.numdam.org/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
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