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http://dx.doi.org/10.4134/JKMS.j160732

ON VOISIN'S CONJECTURE FOR ZERO-CYCLES ON HYPERKÄHLER VARIETIES  

Laterveer, Robert (Institut de Recherche Mathematique Avancee CNRS - Universite de Strasbourg)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 1841-1851 More about this Journal
Abstract
Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of $hyperk{\ddot{a}}hler$ varieties, and we prove this reformulated conjecture for one family of $hyperk{\ddot{a}}hler$ fourfolds.
Keywords
algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; $hyperk{\ddot{a}}hler$ varieties; multiplicative Chow-$K{\ddot{u}}nneth$ decomposition; splitting property; finite-dimensional motive;
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