Cycles over fields of transcendence degree 1

DOI10.1307/mmj/1080837742zbMath1058.14009arXivmath/0211270OpenAlexW1977351717WikidataQ101237764 ScholiaQ101237764MaRDI QIDQ1885573

Kapil Hari Paranjape, Mark L. Green, Phillip A. Griffiths

Publication date: 11 November 2004

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0211270

zbMATH Keywords

Chow groupsalgebraic cyclesAbel-Jacobi mapHodge structuresBloch-Beilinson conjectureintermediate Jacobians

Mathematics Subject Classification ID

Picard schemes, higher Jacobians (14K30) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) (p)-adic cohomology, crystalline cohomology (14F30) (Equivariant) Chow groups and rings; motives (14C15)

Related Items (6)

Non-trivial elements in the Abel-Jacobi kernels of higher-dimensional varieties ⋮ Néron-Severi groups under specialization ⋮ Potential density of rational points on the variety of lines of a cubic fourfold ⋮ Filtrations on Chow groups and transcendence degree ⋮ Albanese kernels and Griffiths groups ⋮ Exterior products of zero-cycles

Cites Work

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• Complete intersections with middle Picard number 1 defined over \({\mathbb{Q}}\)
• The torsion of the group of 0-cycles modulo rational equivalence
• Higher \(l\)-adic Abel-Jacobi mappings and filtrations on Chow groups
• On the periods of certain rational integrals. I, II
• Théorie de Hodge. II. (Hodge theory. II)
• On the motive of an algebraic surface.

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