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Zero-cycles on rational surfaces and Néron-Severi tori. (Russian) Zbl 0556.14027

Let \(X\) be a complete smooth geometrically irreducible rational surface over the perfect field \(k\). In the first part of the paper the birational and arithmetical properties of the Néron-Severi torus associated to \(X\) are studied (see the paper reviewed above Zbl 0556.14026). In some cases, estimations of the Shafarevich-Tate group are obtained.
The second part of the paper deals with bounds for the order of the group \(A_ 0(X)\) of classes of 0-cycles of degree zero modulo rational equivalence.
Reviewer: Alexandru Dimca

MSC:

14M20 Rational and unirational varieties
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
14C25 Algebraic cycles
14C15 (Equivariant) Chow groups and rings; motives
14J25 Special surfaces

Citations:

Zbl 0556.14026
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