Geodesic
Néron model of two-dimensional anisotropic algebraic tori over local fields
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 31-40 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The construction of integral models is necessary for the research on arithmetical properties of algebraic tori. Néron model, having some unique properties, is of special interest among different possible integral models of algebraic tori over local fields. Its definition is not constructive, though. That's why its construction is an important problem. In this paper the problem of explicit construction of Néron model is solved for all two-dimensional anisotropic algebraic tori over local fields.
Mots-clés : algebraic tori, Néron model.
Keywords: Voskresenskii model 
@article{VSGU_2012_9_a3,
     author = {M. V. Grekhov},
     title = {N\'eron model of two-dimensional anisotropic algebraic tori over local fields},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {31--40},
     year = {2012},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2012_9_a3/}
}
TY  - JOUR
AU  - M. V. Grekhov
TI  - Néron model of two-dimensional anisotropic algebraic tori over local fields
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2012
SP  - 31
EP  - 40
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/VSGU_2012_9_a3/
LA  - ru
ID  - VSGU_2012_9_a3
ER  - 
%0 Journal Article
%A M. V. Grekhov
%T Néron model of two-dimensional anisotropic algebraic tori over local fields
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2012
%P 31-40
%N 9
%U http://geodesic.mathdoc.fr/item/VSGU_2012_9_a3/
%G ru
%F VSGU_2012_9_a3
M. V. Grekhov. Néron model of two-dimensional anisotropic algebraic tori over local fields. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 31-40. http://geodesic.mathdoc.fr/item/VSGU_2012_9_a3/

[1] Voskresenskii V. E., Algebraicheskie tory, Nauka, M., 1977, 224 pp. | MR

[2] Platonov V. P., Rapinchuk A. S., Algebraicheskie gruppy i teoriya chisel, Nauka, M., 1991, 656 pp. | MR

[3] Serre J.-P., Local Fields, Springer-Verlag New York Inc., New York, 1979, 241 pp. | MR

[4] Dzh. Kassels, A. Frelikh(red.), Algebraicheskaya teoriya chisel, Mir, M., 1969, 484 pp. | MR

[5] Voskresenskii V. E., Biratsionalnaya geometriya lineinykh algebraicheskikh grupp, MTsNMO, M., 2009, 403 pp.

[6] Popov S. Yu., Standard Integral Models of Algebraic Tori, Preprintreihe des SFB 478 – Geometrische Strukturen in der Mathematik, 2003, 31 pp. | MR

[7] Bosch S., Lütkebohmert W., Raynaud M., Néron Models, Springer-Verlag, Berlin–Heidelberg, 1990, 325 pp. | MR

[8] Ching-Li Ch., Jiu-Kang Yu., Congruences of Néron models for tori and the Artin conductor, National Center for Theoretical Science, National Tsing-Hua University, Hsinchu, Taiwan, 1999, 30 pp.

[9] Voskresenskii V. E., Kunyavskii B. E., Moroz B. Z., “Tselye modeli algebraicheskikh torov”, Algebra i analiz, 14:1 (2002), 35–52 | MR