Chow–Künneth decomposition for 3- and 4-folds fibred by varieties with trivial Chow group of zero-cycles

DOI10.1090/S1056-3911-2014-00616-0zbMath1323.14006arXiv1111.3658OpenAlexW2040201907MaRDI QIDQ2939276

Charles Vial

Publication date: 19 January 2015

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.3658

zbMATH Keywords

Chow groupsalgebraic cyclesmotivesChow-Künneth decomposition

Mathematics Subject Classification ID

Parametrization (Chow and Hilbert schemes) (14C05) Algebraic cycles (14C25) (Equivariant) Chow groups and rings; motives (14C15)

Related Items (16)

ON THE CHOW THEORY OF PROJECTIVIZATIONS ⋮ A family of \(K3\) surfaces having finite-dimensional motive ⋮ On a multiplicative version of Bloch's conjecture ⋮ Some results on a conjecture of Voisin for surfaces of geometric genus one ⋮ A remark on the motive of the Fano variety of lines of a cubic ⋮ Cubic fourfolds, Kuznetsov components, and Chow motives ⋮ Some cubics with finite-dimensional motive ⋮ Some elementary examples of quartics with finite-dimensional motive ⋮ SOME NEW EXAMPLES OF SMASH-NILPOTENT ALGEBRAIC CYCLES ⋮ A family of cubic fourfolds with finite-dimensional motive ⋮ A motivic global Torelli theorem for isogenous \(K3\) surfaces ⋮ Motives of quadric bundles ⋮ Multiplicative Chow-Künneth decompositions and varieties of cohomological \(K3\) type ⋮ A short note on the weak Lefschetz property for Chow groups ⋮ Voisin's conjecture for zero-cycles on Calabi-Yau varieties and their mirrors ⋮ Examples of smash nilpotent cycles on rationally connected varieties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pure motives with representable Chow groups
• Chow groups are finite dimensional, in some sense
• Birational motives. I: Pure birational motives
• Torsion dans le groupe de Chow de codimension deux
• On a conjectural filtration on the Chow groups of an algebraic variety. II: Verification of the conjectures for threefolds which are the product of a surface and a curve
• Finite-dimensional motives and the conjectures of Beilinson and Murre
• Projectors on the intermediate algebraic Jacobians
• Relative Chow–Künneth decompositions for morphisms of threefolds
• Remarks on Correspondences and Algebraic Cycles
• On the motive of an algebraic surface.
• Motives of uniruled 3-folds
• Absolute Chow-Künneth projectors for modular varieties
• Niveau and coniveau filtrations on cohomology groups and Chow groups
• Cycles de codimension 2 etH³non ramifié pour les variétés sur les corps finis
• Motives and representability of algebraic cycles on threefolds over a field

This page was built for publication: Chow–Künneth decomposition for 3- and 4-folds fibred by varieties with trivial Chow group of zero-cycles