Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-14T13:25:39.816Z Has data issue: false hasContentIssue false

Smash nilpotent cycles on varieties dominated by products of curves

Published online by Cambridge University Press:  28 June 2013

Ronnie Sebastian*
Affiliation:
Humboldt Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 10099 Berlin, Germany email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
© The Author(s) 2013 

References

Beauville, A., Sur l’anneau de chow d’une variété abélienne, Math. Ann. 273 (1986), 647651.Google Scholar
Fakhruddin, N., Algebraic cycles on generic abelian varieties, Compositio Math. 100 (1996), 101119.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), 649679.Google Scholar
Herbaut, F., Algebraic cycles on the jacobian of a curve with a linear system of given dimension, Compositio Math. 143 (2007), 883899.Google Scholar
Kahn, B. and Sebastian, R., Smash-nilpotent cycles on abelian 3-folds, Math. Res. Lett. 16 (2009), 10071010.Google Scholar
Kimura, S.-I., Chow groups are finite dimensional, in some sense, Math. Ann. 331 (2005), 173201.Google Scholar
Marini, G., Tautological cycles on jacobian varieties, Collect. Math. 59 (2008), 167190.Google Scholar
Voevodsky, V., A nilpotence theorem for cycles algebraically equivalent to zero, Int. Math. Res. Not. 4 (1995), 187198.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), 265285.Google Scholar