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The arithmetic of the Chow group of zero-cycles. (L’arithmétique du groupe de Chow des zéro-cycles.) (French) Zbl 0870.14002
This article is a comprehensive survey dealing mainly with \(A_0(X)\), the group of zero cycles of degree zero on a smooth projective variety \(X\) modulo rational equivalence. \(X\) is defined over a number field or a local field. The theme of the survey is a pair of conjectures in the first section relating the quotient of \(A_0(X)\) by its maximal divisible subgroup to the Brauer group of \(X\).

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