The arithmetic of the Chow group of zero-cycles

DOI10.5802/jtnb.130zbMath0870.14002OpenAlexW2323873015MaRDI QIDQ1909864

Jean-Louis Colliot-Thélène

Publication date: 24 March 1996

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1995__7_1_51_0

zbMATH Keywords

Brauer grouprational equivalencezero cycles of degree zero

Mathematics Subject Classification ID

Parametrization (Chow and Hilbert schemes) (14C05) Algebraic cycles (14C25) Brauer groups of schemes (14F22)

Related Items (26)

Local-global principle for 0-cycles on fibrations over rationally connected bases ⋮ Index of fibrations and Brauer classes that never obstruct the Hasse principle ⋮ A finer Tate duality theorem for local Galois symbols ⋮ Progress concerning the local-global principle for zero-cycles on algebraic varieties ⋮ Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus de l'espace projectif ⋮ Approximation faible pour les 0-cycles sur un produit de variétés rationnellement connexes ⋮ Divisibility results for zero-cycles ⋮ Une liste de problèmes ⋮ Towards the Brauer-Manin obstruction on varieties fibred over the projective line ⋮ Compatibility of weak approximation for zero-cycles on products of varieties ⋮ A finiteness theorem for zero-cycles over \(p\)-adic fields ⋮ Brauer-Manin obstruction for zero-cycles on certain varieties ⋮ Weak approximation for 0-cycles on a product of elliptic curves ⋮ Zero cycles on fibrations over a curve of arbitrary genus ⋮ A local to global principle for higher zero-cycles ⋮ Degree and the Brauer-Manin obstruction ⋮ Odd order Brauer-Manin obstruction on diagonal quartic surfaces ⋮ Zéro-cycles sur les espaces homogènes et problème de Galois inverse ⋮ On the fibration method for zero-cycles and rational points ⋮ Principe local-global pour les zéro-cycles sur les surfaces réglées ⋮ A Tate duality theorem for local Galois symbols. II. The semi-abelian case ⋮ The Brauer–Manin pairing, class field theory, and motivic homology ⋮ On a filtration of for an abelian variety ⋮ Rigidity for relative 0-cycles ⋮ On Chow and Brauer groups of a product of Mumford curves ⋮ Applications of the fibration method to the Brauer–Manin obstruction to the existence of zero-cycles on certain varieties

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