Some New Examples of Smash-Nilpotent Algebraic Cycles

We study a conjecture, due to Voisin, on 0-cycles on varieties with p g = 1. Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)Künneth decomposition, we provide a general criterion for Calabi-Yau manifolds of dimension at most 5 to verify Voisin's conjecture. We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to 5.

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A family of cubic fourfolds with finite-dimensional motive

Laterveer¹

2018

J. Math. Soc. Japan

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Some New Examples of Smash-Nilpotent Algebraic Cycles

Abstract: ABSTRACT. Voevodsky has conjectured that numerical equivalence and smash-equivalence coincide for algebraic cycles on any smooth projective variety. Building on work of Vial and KahnSebastian, we give some new examples of varieties where Voevodsky's conjecture is verified.

Cited by 3 publications

References 42 publications

Some remarks on the smash-nilpotence conjecture

Some remarks on the smash-nilpotence conjecture

Voisin’s conjecture for zero-cycles on Calabi–Yau varieties and their mirrors

A family of cubic fourfolds with finite-dimensional motive

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