Relations de dépendance et intersections exceptionnelles
Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Talk no. 1032, 40 p.
@incollection{AST_2012__348__149_0,
     author = {Chambert-Loir, Antoine},
     title = {Relations de d\'ependance et intersections exceptionnelles},
     booktitle = {S\'eminaire Bourbaki Volume 2010/2011 Expos\'es 1027-1042. Avec table par noms d'auteurs de 1948/49 \`a 2009/10.},
     series = {Ast\'erisque},
     note = {talk:1032},
     pages = {149--188},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {348},
     year = {2012},
     mrnumber = {3050715},
     zbl = {1273.14068},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2012__348__149_0/}
}
TY  - CHAP
AU  - Chambert-Loir, Antoine
TI  - Relations de dépendance et intersections exceptionnelles
BT  - Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10.
AU  - Collectif
T3  - Astérisque
N1  - talk:1032
PY  - 2012
SP  - 149
EP  - 188
IS  - 348
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2012__348__149_0/
LA  - fr
ID  - AST_2012__348__149_0
ER  - 
%0 Book Section
%A Chambert-Loir, Antoine
%T Relations de dépendance et intersections exceptionnelles
%B Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10.
%A Collectif
%S Astérisque
%Z talk:1032
%D 2012
%P 149-188
%N 348
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2012__348__149_0/
%G fr
%F AST_2012__348__149_0
Chambert-Loir, Antoine. Relations de dépendance et intersections exceptionnelles, in Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Talk no. 1032, 40 p. http://archive.numdam.org/item/AST_2012__348__149_0/

[1] A. Abbes - Hauteurs et discrétude (d'après L. Szpiro, E. Ullmo et S. Zhang), Séminaire Bourbaki, vol. 1996/97, exposé n° 825, Astérisque 245 (1997), p. 141-166. | EuDML | Numdam | MR | Zbl

[2] F. Amoroso & S. David - Le problème de Lehmer en dimension supérieure, J. reine angew. Math. 513 (1999), p. 145-179. | MR | Zbl

[3] F. Amoroso & S. David, Minoration de la hauteur normalisée dans un tore, J. Inst. Math. Jussieu 2 (2003), p. 335-381. | DOI | MR | Zbl

[4] F. Amoroso & S. David, Distribution des points de petite hauteur dans les groupes multiplicatifs, Ann. Sc. Norm. Super. Pisa Cl. Sci. 3 (2004), p. 325-348. | EuDML | Numdam | MR | Zbl

[5] F. Amoroso & E. Viada - Small points on subvarieties of a torus, Duke Math. J. 150 (2009), p. 407-442. | DOI | MR | Zbl

[6] J. Ax- Some topics in differential algebraic geometry. I. Analytic subgroups of algebraic groups, Amer. J. Math. 94 (1972), p. 1195-1204. | DOI | MR | Zbl

[7] D. Bertrand - Special points and Poincaré biextensions, prépublication arXiv:1104.5178.

[8] F. A. Bogomolov - Points of finite order on abelian varieties, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), p. 782-804, 973. | MR | Zbl

[9] E. Bombieri - The Mordell conjecture revisited, Ann. Scuola Norm. Sup. Pisa CI. Sci. 17 (1990), p. 615-640. | EuDML | Numdam | MR | Zbl

[10] E. Bombieri & W. Gubler - Heights in Diophantine geometry, New Mathematical Monographs, vol. 4, Cambridge Univ. Press, 2006. | MR | Zbl

[11] E. Bombieri, P. Habegger, D. Masser & U. Zannier - A note on Maurin's theorem, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 21 (2010), p. 251-260. | DOI | MR | Zbl

[12] E. Bombieri, D. Masser & U. Zannier - Intersecting a curve with algebraic subgroups of multiplicative groups, Int. Math. Res. Not. (1999), n° 20, p. 1119-1140. | DOI | MR | Zbl

[13] E. Bombieri, D. Masser & U. Zannier, Intersecting curves and algebraic subgroups : conjectures and more results, Trans. Amer. Math. Soc. 358 (2006), p. 2247-2257. | DOI | MR | Zbl

[14] E. Bombieri, D. Masser & U. Zannier, Anomalous subvarieties-structure theorems and applications, Int. Math. Res. Not. (2007), n° 19, p. 1-33. | MR | Zbl

[15] E. Bombieri, D. Masser & U. Zannier, Intersecting a plane with algebraic subgroups of multiplicative groups, Ann. Sc. Norm. Super. Pisa CI. Sci. 7 (2008), p. 51-80. | EuDML | Numdam | MR | Zbl

[16] E. Bombieri, D. Masser & U. Zannier, On unlikely intersections of complex varieties with tori, Acta Arith. 133 (2008), p. 309-323. | DOI | EuDML | MR | Zbl

[17] E. Bombieri & U. Zannier - Algebraic points on subvarieties of 𝐆 m n , Int. Math. Res. Not. (1995), n° 7, p. 333-347. | DOI | MR | Zbl

[18] J.-B. Bost, H. Gillet & C. Soulé - Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), p. 903-1027. | DOI | MR | Zbl

[19] M. Carrizosa - Petits points et multiplication complexe, Int. Math. Res. Not. (2009), n° 16, p. 3016-3097. | MR | Zbl

[20] S. David & M. Hindry - Minoration de la hauteur de Néron-Tate sur les variétés abéliennes de type C. M, J. reine angew. Math. 529 (2000), p. 1-74. | DOI | MR | Zbl

[21] S. David & P. Philippon - Minorations des hauteurs normalisées des sous-variétés de variétés abéliennes, in Number theory (Tiruchirapalli, 1996), Contemp. Math., vol. 210, Amer. Math. Soc., 1998, p. 333-364. | DOI | MR | Zbl

[22] S. David & P. Philippon, Minorations des hauteurs normalisées des sous-variétés des tores, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999), p. 489-543. | EuDML | Numdam | MR | Zbl

[23] S. David & P. Philippon, Sous-variétés de torsion des variétés semi-abéliennes, C. R. Acad. Sci.Paris Sér. I Math. 331 (2000), p. 587-592. | DOI | MR | Zbl

[24] E. Delsinne - Le problème de Lehmer relatif en dimension supérieure, Ann. Sci. Éc. Norm. Super. 42 (2009), p. 981-1028. | DOI | EuDML | Numdam | MR | Zbl

[25] E. Dobrowolski - On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), p. 391-401. | DOI | EuDML | MR | Zbl

[26] G. Faltings - Diophantine approximation on abelian varieties, Ann. of Math. 133 (1991), p. 549-576. | DOI | MR | Zbl

[27] A. Galateau - Le problème de Bogomolov effectif sur les variétés abéliennes, Algebra Number Theory 4 (2010), p. 547-598. | DOI | MR | Zbl

[28] P. Habegger - Intersecting subvarieties of 𝐆 m n with algebraic subgroups, Math. Ann. 342 (2008), p. 449-466. | DOI | MR | Zbl

[29] P. Habegger, A Bogomolov property for curves modulo algebraic subgroups, Bull. Soc. Math. France 137 (2009), p. 93-125. | DOI | EuDML | Numdam | MR | Zbl

[30] P. Habegger, Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension, Invent. Math. 176 (2009), p. 405-447. | DOI | MR | Zbl

[31] P. Habegger, On the bounded height conjecture, Int. Math. Res. Not. (2009), n° 5, p. 860-886. | MR | Zbl

[32] M. Hindry - Autour d'une conjecture de Serge Lang, Invent. Math. 94 (1988), p. 575-603. | DOI | EuDML | MR | Zbl

[33] M. Hindry & J. H. Silverman - Diophantine geometry, Graduate Texts in Math., vol. 201, Springer, 2000. | DOI | MR | Zbl

[34] E. Hrushovski - The Manin-Mumford conjecture and the model theory of difference fields, Ann. Pure Appl. Logic 112 (2001), p. 43-115. | DOI | MR | Zbl

[35] J. Kirby - The theory of the exponential differential equations of semiabelian varieties, Selecta Math. (N.S.) 15 (2009), p. 445-486. | DOI | MR | Zbl

[36] S. Lang - Fundamentals of Diophantine geometry, Springer, 1983. | DOI | MR | Zbl

[37] M. Laurent - Minoration de la hauteur de Néron-Tate, in Seminar on number theory, Paris 1981-82 (Paris, 1981/1982), Progr. Math., vol. 38, Birkhäuser, 1983, p. 137-151. | MR | Zbl

[38] M. Laurent, Équations diophantiennes exponentielles, Invent. Math. 78 (1984), p. 299-327. | DOI | EuDML | MR | Zbl

[39] P. Liardet - Sur une conjecture de Serge Lang, in Journées Arithmétiques de Bordeaux (Conf, Univ. Bordeaux, Bordeaux, 1974), Soc. Math. France, 1975, p. 187-210. Astérisque, Nos. 24-25. | Numdam | MR | Zbl

[40] D. Masser & U. Zannier - Torsion anomalous points and families of elliptic curves, Amer. J. Math. 132 (2010), p. 1677-1691. | MR | Zbl

[41] D. Masser & U. Zannier, Torsion points on families of squares of elliptic curves, Math. Ann. 352 (2012), p. 453-484. | DOI | MR | Zbl

[42] G. Maurin - Courbes algébriques et équations multiplicatives, Math. Ann. 341 (2008), p. 789-824. | DOI | MR | Zbl

[43] G. Maurin, Équations multiplicatives sur les sous-variétés des tores, Int. Math. Res. Not. (2011), n° 23, p. 5259-5366. | MR | Zbl

[44] M. Mcquillan - Division points on semi-abelian varieties, Invent. Math. 120 (1995), p. 143-159. | DOI | EuDML | MR | Zbl

[45] A. Ogus - Hodge cycles and crystalline cohomology, Lecture Notes in Math. 900 (1981), p. 357-414. | Zbl

[46] J. Pila - O-minimality and the André-Oort conjecture for n , Ann. of Math. 173 (2011), p. 1779-1840. | DOI | Zbl

[47] J. Pila & U. Zannier - Rational points in periodic analytic sets and the Manin-Mumford conjecture, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008), p. 149-162. | DOI | Zbl

[48] R. Pink - l -adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture, J. reine angew. Math. 495 (1998), p. 187-237. | Zbl

[49] R. Pink, A combination of the conjectures of Mordell-Lang and André-Oort, in Geometric methods in algebra and number theory, Progr. Math., vol. 235, Birkhäuser, 2005, p. 251-282. | Zbl

[50] R. Pink, A common generalization of the conjectures of André-Oort, Manin-Mumford, and Mordell-Lang, 2005, Tech. report, ETH, Zürich, 2005, http://www.math.ethz.ch/˜pink/ftp/A0MMML.pdf

[51] R. Pink & D. Roessler - On Hrushovski's proof of the Manin-Mumford conjecture, in Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), Higher Ed. Press, 2002, p. 539-546. | Zbl

[52] R. Pink & D. Roessler, On ψ -invariant subvarieties of semiabelian varieties and the Manin-Mumford conjecture, J. Algebraic Geom. 13 (2004), p. 771-798. | DOI | Zbl

[53] B. Poizat - L'égalité au cube, J. Symbolic Logic 66 (2001), p. 1647-1676. | DOI | Zbl

[54] B. Poonen - Mordell-Lang plus Bogomolov, Invent. Math. 137 (1999), p. 413-425. | DOI | Zbl

[55] Z. Ran - On subvarieties of abelian varieties, Invent. Math. 62 (1981), p. 459-479. | DOI | EuDML | Zbl

[56] M. Raynaud - Around the Mordell conjecture for function fields and a conjecture of Serge Lang, in Algebraic geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., vol. 1016, Springer, 1983, p. 1-19. | DOI | Zbl

[57] M. Raynaud, Courbes sur une variété abélienne et points de torsion, Invent. Math. 71 (1983), p. 207-233. | DOI | EuDML | Zbl

[58] G. Rémond - Inégalité de Vojta en dimension supérieure, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000), p. 101-151. | EuDML | Numdam | Zbl

[59] G. Rémond, Sur le théorème du produit, J. Théor. Nombres Bordeaux 13 (2001), p. 287-302. | DOI | EuDML | Numdam | Zbl

[60] G. Rémond, Sur les sous-variétés des tores, Compositio Math. 134 (2002), p. 337-366. | DOI | Zbl

[61] G. Rémond, Approximation diophantienne sur les variétés semi-abéliennes, Ann. Sci. École Norm. Sup. 36 (2003), p. 191-212. | DOI | EuDML | Numdam | Zbl

[62] G. Rémond, Inégalité de Vojta généralisée, Bull. Soc. Math. France 133 (2005), p. 459-495. | DOI | EuDML | Numdam | Zbl

[63] G. Rémond, Intersection de sous-groupes et de sous-variétés. I, Math. Ann. 333 (2005), p. 525-548. | DOI | Zbl

[64] G. Rémond, Intersection de sous-groupes et de sous-variétés. II, J. Inst. Math. Jussieu 6 (2007), p. 317-348. | DOI | Zbl

[65] G. Rémond, Autour de la conjecture de Zilber-Pink, J. Théor. Nombres Bordeaux 21 (2009), p. 405-414. | DOI | EuDML | Numdam | Zbl

[66] G. Rémond, Intersection de sous-groupes et de sous-variétés. III, Comment. Math. Helv. 84 (2009), p. 835-863. | DOI | Zbl

[67] G. Rémond & E. Viada - Problème de Mordell-Lang modulo certaines sous-variétés abéliennes, Int. Math. Res. Not. (2003), n° 35, p. 1915-1931. | DOI | Zbl

[68] D. Roessler - A note on the Manin-Mumford conjecture, in Number fields and function fields-two parallel worlds, Progr. Math., vol. 239, Birkhäuser, 2005, p. 311-318. | DOI | Zbl

[69] P. Sarnak & S. Adams - Betti numbers of congruence groups, Israel J. Math. 88 (1994), p. 31-72. | DOI | Zbl

[70] H. P. Schlickewei - Lower bounds for heights on finitely generated groups, Monatsh. Math. 123 (1997), p. 171-178. | DOI | EuDML | Zbl

[71] J-P. Serre - Abelian l-adic representations and elliptic curves, McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute, W. A. Benjamin, Inc., New York-Amsterdam, 1968. | Zbl

[72] J-P. Serre, Lectures on the Mordell-Weil theorem, third éd., Aspects of Mathematics, Friedr. Vieweg & Sohn, 1997. | Zbl

[73] Y. T. Siu - An effective Matsusaka big theorem, Ann. Inst. Fourier (Grenoble) 43 (1993), p. 1387-1405. | DOI | EuDML | Numdam | Zbl

[74] E. Ullmo - Positivité et discrétion des points algébriques des courbes, Ann. of Math. 147 (1998), p. 167-179. | DOI | Zbl

[75] E. Viada - The intersection of a curve with a union of translated codimension-two subgroups in a power of an elliptic curve, Algebra Number Theory 2 (2008), p. 249-298. | DOI | Zbl

[76] E. Viada,The optimality of the bounded height conjecture, J. Théor. Nombres Bordeaux 21 (2009), p. 771-786. | DOI | EuDML | Numdam

[77] E. Viada, Lower bounds for the normalized height and non-dense subsets of subvarieties of abelian varieties, Int. J. Number Theory 6 (2010), p. 471-499. | DOI | Zbl

[78] P. Vojta - Integral points on subvarieties of semiabelian varieties. I, Invent. Math. 126 (1996), p. 133-181. | DOI | Zbl

[79] U. Zannier - Lecture notes on Diophantine analysis, Appunti. Scuola Normale Superiore di Pisa (Nuova Serie), vol. 8, Edizioni della Normale, Pisa, 2009. | Zbl

[80] S.-W. Zhang - Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995), p. 187-221. | DOI | Zbl

[81] S.-W. Zhang, Equidistribution of small points on abelian varieties, Ann. of Math. 147 (1998), p. 159-165. | DOI | Zbl

[82] B. Zilber - Exponential sums equations and the Schanuel conjecture, J. London Math. Soc. 65 (2002), p. 27-44. | DOI | Zbl