Chow groups

General Introduction
See also Algebraic cycles, Higher Chow groups, Chow homology, Chow groups with coefficients, Chow cohomology
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Search results
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Online References
Gillet: Ktheory and Intersection theory (looks excellent)
Something might be in here.
A very intereting paper by Joshua on motivic DGA.
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Paper References
Levine in Ktheory handbook.
My own notes from Totaro's course, spring 2008.
Seminaire Chevalley: Anneaux de Chow et applications (1958)
Soulé et al: Lectures on Arakelov Geometry. First chapter treats intersection theory for an arbitrary regular noetherian finitedimensional scheme.
What about Bloch: An elementary presentation... (in Motives vol)?
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Definition
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Properties
Homotopy invariance and localization. See Levine (page 443). Also MayerVietoris long exact seq. Products. Projective bundle formula.
The Kunneth formula fails for Chow groups, at least over the complex numbers. Counterexample: See Totaro's Algebraic cycles exam, there one shows that the natural homomorphism is not surjective.
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
Several papers by Akhtar on Ktheory archive.
http://mathoverflow.net/questions/99897/examplesofchowringsofsurfaces mentions surfaces over finite fields
arXiv:1207.4703 On the Chow groups of certain geometrically rational 5folds fra arXiv Front: math.NT av Ambrus Pal We give an explicit regular model for the quadric fibration studied in Pirutka (2011). As an application we show that this construction furnishes a counterexample for the integral Tate conjecture in any odd characteristic for some sufficiently large finite field. We study the étale cohomology of this regular model, and as a consequence we derive that these counterexamples are not torsion.
arXiv:1206.2704 On the torsion of Chow groups of SeveriBrauer varieties fra arXiv Front: math.AG av Sanghoon Baek For a large class of central simple algebras we provide upper bounds for the annihilators of the torsion subgroups of the Chow groups of the corresponding SeveriBrauer varieties.
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History and Applications
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Some Research Articles
The Chow groups and the motive of the Hilbert scheme of points on a surface, by Mark Andrea de Cataldo and Luca Migliorini: K0415
Saito: On the bijectivity of some cycle maps (in Motives vol)
Pedrini and Weibel: Ktheory and Chow groups on singular varieties (1986)
Roberts: Chow's moving lemma. (Appendix to Kleiman's Motives article in the Oslo volume)
Saito et al: We study the higher Chow groups CH^2(X,1) and CH^3(X,2) of smooth, projective algebraic surfaces over a field of char 0.
The oriented Chow ring, by J. Fasel
Chow rings of excellent quadrics, by Nobuaki Yagita: K0787
MR1780429 (2001m:11106) Otsubo, Noriyuki(JTOKYO) Selmer groups and zerocycles on the Fermat quartic surface.
Soulé: Groupes de Chow et Kthéorie de varietes sur un corps fini (1984)
Biswat and Srinivas: The Chow ring of a singular surface
Kresch: Canonical rational equivalence of intersections of divisors (1999)
Roberts: Recent developments on Serre's multiplicity conjectures: Gabber's proof of the nonnegativity conjecture (1998)
Complex varieties for which the Chow group mod n is not finite (2002)
Laterveer: Algebraic varieties with small Chow groups. Discusses things related to "representability of Chow groups", and the Hodge conjecture.
Green, Griffiths: Formal Deformation of Chow Groups. In Abel volume.
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Other Information
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