Points de petite hauteur sur les variétés semi-abéliennes
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 6, p. 789-821
@article{ASENS_2000_4_33_6_789_0,
     author = {Chambert-Loir, Antoine},
     title = {Points de petite hauteur sur les vari\'et\'es semi-ab\'eliennes},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {4e s{\'e}rie, 33},
     number = {6},
     year = {2000},
     pages = {789-821},
     doi = {10.1016/s0012-9593(00)01053-3},
     zbl = {01594090},
     mrnumber = {2002e:14037},
     language = {fr},
     url = {http://www.numdam.org/item/ASENS_2000_4_33_6_789_0}
}
Chambert-Loir, Antoine. Points de petite hauteur sur les variétés semi-abéliennes. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 6, pp. 789-821. doi : 10.1016/s0012-9593(00)01053-3. http://www.numdam.org/item/ASENS_2000_4_33_6_789_0/

[1] Bedford E., Taylor B., A new capacity for plurisubharmonic functions, Acta Math. 149 (1982) 1-40. | MR 84d:32024 | Zbl 0547.32012

[2] Bertrand D., Minimal heights and polarizations on group varieties, Duke Math. J. 80 (1) (1995) 223-250. | MR 97a:11091 | Zbl 0847.11036

[3] Bilu Yu., Limit distribution of small points on algebraic tori, Duke Math. J. 89 (3) (1997) 465-476. | MR 98m:11067 | Zbl 0918.11035

[4] Bogomolov F.A., Points of finite order on abelian varieties, Izv. Akad. Nauk. SSSR Ser. Mat. 44 (4) (1980) 782-804, 973. | MR 81m:14031 | Zbl 0453.14018

[5] Bombieri E., Zannier U., Algebraic points on subvarieties of Gnm, Int. Math. Res. Notices 7 (1995) 333-347. | MR 96h:11061 | Zbl 0848.11030

[6] Bosch S., Lütkebohmert W., Raynaud M., Néron Models, Ergeb., Vol. 21, Springer-Verlag, 1990. | MR 91i:14034 | Zbl 0705.14001

[7] Bost J.-B., Gillet H., Soulé C., Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994) 903-1027. | MR 95j:14025 | Zbl 0973.14013

[8] Chambert-Loir A., Géométrie d'Arakelov et hauteurs canoniques sur des variétés semi-abéliennes, Math. Ann. 314 (1999) 381-401. | MR 2000e:14032 | Zbl 0944.14010

[9] Chambert-Loir A., Tschinkel Yu., Torseurs arithmétiques et espaces fibrés, E-print, math.NT/9901006, 1999.

[10] David S., Philippon P., Minorations des hauteurs normalisées des sous-variétés de variétés abéliennes, in : International Conference on Discrete Mathematics and Number Theory (Tiruchirapelli, 1996), Contemp. Math., 1998, pp. 333-364. | MR 98j:11044 | Zbl 0899.11027

[11] Demailly J.-P., Monge-Ampère operators, Lelong numbers and intersection theory, in : Complex Analysis and Geometry, Univ. Ser. Math., Plenum, New York, 1993, pp. 115-193. | MR 94k:32009 | Zbl 0792.32006

[12] Gillet H., Soulé C., Arithmetic intersection theory, Publ. Math. Inst. Hautes Études Sci. 72 (1990) 94-174. | Numdam | MR 92d:14016 | Zbl 0741.14012

[13] Hartshorne R., Algebraic Geometry, Graduate Texts in Math., Vol. 52, Springer-Verlag, 1977. | MR 57 #3116 | Zbl 0367.14001

[14] Hindry M., Autour d'une conjecture de Serge Lang, Invent. Math. 93 (1988) 419-450. | MR 89k:11044 | Zbl 0638.14026

[15] Klimek M., Pluripotential Theory, London Math. Society Monographs, Vol. 6, Clarendon Press, 1991. | MR 93h:32021 | Zbl 0742.31001

[16] Knop F., Lange H., Some remarks on compactifications of commutative algebraic groups, Comment. Math. Helv. 60 (1985) 497-507. | MR 87e:14042 | Zbl 0587.14030

[17] Künnemann K., Higher Picard varieties and the height pairing, Amer. J. Math. 118 (4) (1996) 781-797. | MR 97d:14064 | Zbl 0876.14006

[18] Künnemann K., Projective regular models for abelian varieties, semi-stable reduction, and the height pairing, Duke Math. J. 95 (1) (1998) 161-212. | Zbl 0955.14017

[19] Laurent M., Équations diophantiennes exponentielles, Invent. Math. 78 (1984) 299-327. | MR 86j:11062 | Zbl 0554.10009

[20] Lawton W.M., A generalization of a theorem of Kronecker, J. Sci. Fac. Chiang Mai Univ. 4 (1977) 15-23. | Zbl 0447.12004

[21] Maillot V., Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables, Mémoires de la Soc. Math. de France 80 (2000). | Numdam | MR 2001j:14037 | Zbl 0963.14009

[22] Mcquillan M., Division points on semi-abelian varieties, Invent. Math. 120 (1995) 143-159. | MR 96b:14020 | Zbl 0848.14022

[23] Philippon P., Sur des hauteurs alternatives, I, Math. Ann. 289 (1991) 255-283. | MR 92m:11061 | Zbl 0726.14017

[24] Poonen B., Mordell-Lang plus Bogomolov, Invent. Math. 137 (2) (1999) 213-245. | MR 2001c:11070 | Zbl 0995.11040

[25] Raynaud M., Sous-variétés d'une variété abélienne et points de torsion, in : Artin M., Tate J. (Eds.), Arithmetic and Geometry. Papers dedicated to I.R. Shafarevich, Progr. Math., Vol. 35, Birkhäuser, 1983, pp. 327-352. | MR 85k:14022 | Zbl 0581.14031

[26] Schmidt W., Heights of points on subvarieties of Gnm, in : Number Theory (Paris 1993-1994), London Math. Soc. Lecture Note Ser., Vol. 235, Cambridge Univ. Press, 1996, pp. 157-187. | Zbl 0917.11023

[27] Serre J.-P., Quelques propriétés des groupes algébriques commutatifs, in : Astérisque, Vol. 69-70, Astérisque, Soc. Math. France, 1979, pp. 191-202. | MR 82k:10041

[28] Soulé C., Abramovich D., Burnol J.-F., Kramer J., Lectures on Arakelov Geometry, Cambridge Studies in Advances Mathematics, Vol. 33, Cambridge University Press, 1992. | MR 94e:14031 | Zbl 0812.14015

[29] Szpiro L., Ullmo E., Zhang S.-W., Équidistribution des petits points, Invent. Math. 127 (1997) 337-348. | MR 98i:14027 | Zbl 0991.11035

[30] Ullmo E., Positivité et discrétion des points algébriques des courbes, Ann. of Math. 147 (1) (1998) 167-179. | MR 99e:14031 | Zbl 0934.14013

[31] Vojta P., Integral points on subvarieties of semiabelian varieties, I, Invent. Math. 126 (1996) 133-181. | MR 98a:14034 | Zbl 1011.11040

[32] Vojta P., Integral points on subvarieties of semiabelian varieties, II, Amer. J. Math. 121 (2) (1999) 283-313. | MR 2000d:11074 | Zbl 1018.11027

[33] Zhang S.-W., Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995) 187-221. | MR 95c:14020 | Zbl 0861.14018

[34] Zhang S.-W., Small points and adelic metrics, J. Algebraic Geometry 4 (1995) 281-300. | MR 96e:14025 | Zbl 0861.14019

[35] Zhang S.-W., Equidistribution of small points on abelian varieties, Ann. of Math. 147 (1) (1998) 159-165. | MR 99e:14032 | Zbl 0991.11034