Kunyavskiĭ, B. È.; Tsfasman, M. A. Zero-cycles on rational surfaces and Néron-Severi tori. (Russian) Zbl 0556.14027 Izv. Akad. Nauk SSSR, Ser. Mat. 48, No. 3, 631-654 (1984). 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 Cited in 3 ReviewsCited in 5 Documents 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 Keywords:zero cycles; rational surface; Néron-Severi torus Citations:Zbl 0556.14026 PDFBibTeX XMLCite \textit{B. È. Kunyavskiĭ} and \textit{M. A. Tsfasman}, Izv. Akad. Nauk SSSR, Ser. Mat. 48, No. 3, 631--654 (1984; Zbl 0556.14027)