Geodesic
Zero-cycles on rational surfaces and N\'eron--Severi tori
Izvestiya. Mathematics , Tome 24 (1985) no. 3, pp. 583-603.

Voir la notice de l'article provenant de la source Math-Net.Ru

Birational and arithmetic properties of the algebraic torus dual to the Picard module of a rational surface are studied. The results are used to estimate the order of the group of classes of 0-cycles of degree zero modulo rational equivalence. Bibliography: 20 titles. 
@article{IM2_1985_24_3_a7,
     author = {B. \`E. Kunyavskii and M. A. Tsfasman},
     title = {Zero-cycles on rational surfaces and {N\'eron--Severi} tori},
     journal = {Izvestiya. Mathematics },
     pages = {583--603},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a7/}
}
TY  - JOUR
AU  - B. È. Kunyavskii
AU  - M. A. Tsfasman
TI  - Zero-cycles on rational surfaces and N\'eron--Severi tori
JO  - Izvestiya. Mathematics 
PY  - 1985
SP  - 583
EP  - 603
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a7/
LA  - en
ID  - IM2_1985_24_3_a7
ER  - 
%0 Journal Article
%A B. È. Kunyavskii
%A M. A. Tsfasman
%T Zero-cycles on rational surfaces and N\'eron--Severi tori
%J Izvestiya. Mathematics 
%D 1985
%P 583-603
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a7/
%G en
%F IM2_1985_24_3_a7
B. È. Kunyavskii; M. A. Tsfasman. Zero-cycles on rational surfaces and N\'eron--Severi tori. Izvestiya. Mathematics , Tome 24 (1985) no. 3, pp. 583-603. http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a7/

[1] Manin Yu. I., Kubicheskie formy, Nauka, M., 1972 | MR

[2] Tsfasman M. A., “Arifmetika rassloenii na koniki”, Uspekhi matem. nauk, 37:2 (1982), 239–240 | MR | Zbl

[3] Kunyavskii B. E., Tsfasman M. A., “Tor Nerona–Severi ratsionalnoi poverkhnosti”, Uspekhi matem. nauk, 37:4 (1982), 163–164 | MR | Zbl

[4] Manin Yu. I., “Ratsionalnye poverkhnosti nad sovershennymi polyami”, Publ. Math. IHES, 30 (1966), 55–113 | MR

[5] Iskovskikh V. L., “Minimalnye modeli ratsionalnykh poverkhnostei nad proizvolnymi polyami”, Izv. AN SSSR. Ser. matem., 43:1 (1979), 19–43 | MR | Zbl

[6] Tsen C. C., “Divisionalgebren über Funktionenkörpern”, Nach. Ges. Wiss. Gottingen, 1933 | Zbl

[7] Voskresenskii V. E., Algebraicheskie tory, Nauka, M., 1977 | MR

[8] Tate J. T., “The cohomology groups of tori in finite Galois extensions of number fields”, Nagoya Math. J., 27 (1966), 709–719 | MR | Zbl

[9] Colliot-Thélène J. L., Sansuc J. J., “On the Chow groups of certain rational surfaces: a sequel to a paper of S. Block”, Duke Math. J., 48:2 (1981), 421–447 | DOI | MR | Zbl

[10] Voskresenskii V. E., “Proektivnye invariantnye modeli Demazyura”, Izv. AN SSSR. Ser. matem., 46:2 (1982), 195–210 | MR | Zbl

[11] Kunyavskii B. E., “O torakh s bikvadratichnym polem razlozheniya”, Izv. AN SSSR. Ser. matem., 42:3 (1978), 580–587 | MR | Zbl

[12] Bloch S., “On the Chow groups of certain rational surfaces”, Ann. Sci. Éc. Norm. Sup., 14:1 (1981), 41–59 | MR | Zbl

[13] Colliot-Thélène J. L., The Chow group of rational surfaces, Preprint 25/2/1982, Cambridge | MR | Zbl

[14] Swinnerton-Dyer H. P. F., Rational equivalence and $R$-equivalence on cubic surfaces, Preprint, Cambridge, 1980 | Zbl

[15] Colliot-Thélène J. L., Ischebeck F., “L'équivalence rationnelle sur les cycles de dimension zéro des variétés algébriques réelles”, Comp. Rend. Acad. Sci., 292:15 (1981), 723–725 | MR | Zbl

[16] Iskovskikh V. A., “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh”, Matem. sb., 74:4 (1967), 608–638 | Zbl

[17] Sansuc J. J., Post Duke: quelques calculs autour de {\rm$\text{Sh}(A_0(X))$}, avec I'appendice par Colliot-Thélène J.-L., Prepublication, Éc. Norm. Sup., Paris, 22/11/1981 | Zbl

[18] Cepp Zh.- P., Kurs arifmetiki, Mir, M., 1972 | MR

[19] Sansuc J.-J., L'exemple de Tsfasman, Prepublication, Éc. Norm. Sup., Paris, 16/2/1982 | Zbl

[20] Tsfasman M. A., “Arifmetika osobykh poverkhnostei del-Petstso”, Uspekhi matem. nauk, 38:6 (1983), 131–132 | MR | Zbl