Motives and representability of algebraic cycles on threefolds over a field

DOI10.1090/S1056-3911-2011-00548-1zbMath1256.14007arXiv0806.0173MaRDI QIDQ5388776

Sergey O. Gorchinskiy, Vladimir Guletskii

Publication date: 20 April 2012

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

Full work available at URL: https://arxiv.org/abs/0806.0173

Mathematics Subject Classification ID

(3)-folds (14J30) Fano varieties (14J45) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items (16)

Integral Chow motives of threefolds with $K$-motives of unit type ⋮ The motive of the Fano surface of lines ⋮ Motives of derived equivalent \(K3\) surfaces ⋮ Some desultory remarks concerning algebraic cycles and Calabi-Yau threefolds ⋮ Geometric phantom categories ⋮ Chow–Künneth decomposition for 3- and 4-folds fibred by varieties with trivial Chow group of zero-cycles ⋮ Non-trivial elements in the Abel-Jacobi kernels of higher-dimensional varieties ⋮ Étale monodromy and rational equivalence for -cycles on cubic hypersurfaces in ⋮ The transcendental motive of a cubic fourfold ⋮ Some remarks concerning Voevodsky's nilpotence conjecture ⋮ A motivic global Torelli theorem for isogenous \(K3\) surfaces ⋮ The generalized Franchetta conjecture for some hyper-Kähler varieties. II ⋮ Motives of moduli spaces on \(K3\) surfaces and of special cubic fourfolds ⋮ Albanese kernels and Griffiths groups ⋮ The motive of a smooth theta divisor ⋮ Corrigendum to “Motives and representability of algebraic cycles on threefolds over a field”

Cites Work

• Chow groups are finite dimensional, in some sense
• Semistable degenerations of Enriques' and hyperelliptic surfaces
• Motivic decomposition and intersection Chow groups. I.
• Finite-dimensional motives and the conjectures of Beilinson and Murre
• Remarks on Correspondences and Algebraic Cycles
• $ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM
• On the motive of an algebraic surface.
• On the continuous part of codimension 2 algebraic cycles on three-dimensional varieties
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