Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: Un théorème de finitude pour la torsion. (The codimension two Chow group of varieties defined over a number field: A finiteness theorem for the torsion)

DOI10.1007/BF01232266zbMath0752.14004OpenAlexW2011111761MaRDI QIDQ1177898

Wayne Raskind, Jean-Louis Colliot-Thélène

Publication date: 26 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143912

zbMATH Keywords

codimension two cyclesrational equivalencemodulo rational equivalencetorsion group of Chow group

Mathematics Subject Classification ID

Parametrization (Chow and Hilbert schemes) (14C05) Global ground fields in algebraic geometry (14G25)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• K-theory of discrete valuation rings
• Hilbert's theorem 90 for \(K^ 2\), with application to the Chow groups of rational surfaces
• Universal exactness in algebraic K-theory
• On \(K_1\) of curves over global fields. Appendix by C. Weibel
• Torsion dans le groupe de Chow de codimension deux
• Gersten's conjecture for the K-theory with torsion coefficients of a discrete valuation ring
• Torsion in \(K_ 2\) of fields
• Riemann-Roch theorems for higher algebraic K-theory
• On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch
• The K-theory of hereditary categories
• Zero-cycles on rational surfaces over number fields
• The relative form of Gersten's conjecture over a discrete valuation ring: The smooth case
• Algebraic K-theory and classfield theory for arithmetic surfaces
• Unramified class field theory of arithmetical surfaces
• Algebraic approximation of structures over complete local rings
• On Milnor K-groups attached to semi-Abelian varieties
• On the Chow groups of certain rational surfaces
• Remarks on Correspondences and Algebraic Cycles
• A Hasse principle for two dimensional global fields.
• 0-cycles de degré 0 sur les surfaces fibrées en coniques.
• K-cohomology of regular schemes
• Some theorems on the k-theory of coherent sheaves
• Bertini theorems for hypersurface sections containing a subscheme