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Smash nilpotent cycles on varieties dominated by products of curves

Part of: Abelian varieties and schemes Cycles and subschemes

Published online by Cambridge University Press:  28 June 2013

Ronnie Sebastian
Ronnie Sebastian*
Affiliation:
Humboldt Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 10099 Berlin, Germany email [email protected]
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Abstract

Voevodsky conjectured that numerical equivalence and smash equivalence coincide on a smooth projective variety. We prove the conjecture for 1-cycles on varieties dominated by products of curves.

Keywords

algebraic cyclessmash nilpotenceabelian varieties

MSC classification

Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14C25: Algebraic cycles 14K12: Subvarieties
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 9 , September 2013 , pp. 1511 - 1518
Copyright
© The Author(s) 2013 

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References

Beauville, A., Sur l’anneau de chow d’une variété abélienne, Math. Ann. 273 (1986), 647–651.Google Scholar
Fakhruddin, N., Algebraic cycles on generic abelian varieties, Compositio Math. 100 (1996), 101–119.Google Scholar
Fulton, W., Intersection theory (Springer, Berlin, 1997).Google Scholar
Gross, B. H. and Schoen, C., The modified diagonal cycle on the triple product of a pointed curve, Ann. Inst. Fourier (Grenoble) 45 (1995), 649–679.Google Scholar
Herbaut, F., Algebraic cycles on the jacobian of a curve with a linear system of given dimension, Compositio Math. 143 (2007), 883–899.Google Scholar
Kahn, B. and Sebastian, R., Smash-nilpotent cycles on abelian 3-folds, Math. Res. Lett. 16 (2009), 1007–1010.Google Scholar
Kimura, S.-I., Chow groups are finite dimensional, in some sense, Math. Ann. 331 (2005), 173–201.Google Scholar
Marini, G., Tautological cycles on jacobian varieties, Collect. Math. 59 (2008), 167–190.Google Scholar
Voevodsky, V., A nilpotence theorem for cycles algebraically equivalent to zero, Int. Math. Res. Not. 4 (1995), 187–198.Google Scholar
Voisin, C., Remarks on zero-cycles of self-products of varieties, in Moduli of vector bundles (Sanda, 1994; Kyoto, 1994), Lecture Notes in Pure and Applied Mathematics, vol. 179 (Marcel Dekker, New York, 1996), 265–285.Google Scholar