@article{ASENS_2007_4_40_6_951_0, author = {Ratazzi, Nicolas}, title = {Borne sur la torsion dans les vari\'et\'es ab\'eliennes de type {CM}}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {951--983}, publisher = {Elsevier}, volume = {4e s{\'e}rie, 40}, number = {6}, year = {2007}, doi = {10.1016/j.ansens.2007.10.002}, mrnumber = {2419854}, zbl = {1140.14041}, language = {fr}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2007.10.002/} }
TY - JOUR AU - Ratazzi, Nicolas TI - Borne sur la torsion dans les variétés abéliennes de type CM JO - Annales scientifiques de l'École Normale Supérieure PY - 2007 SP - 951 EP - 983 VL - 40 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2007.10.002/ DO - 10.1016/j.ansens.2007.10.002 LA - fr ID - ASENS_2007_4_40_6_951_0 ER -
%0 Journal Article %A Ratazzi, Nicolas %T Borne sur la torsion dans les variétés abéliennes de type CM %J Annales scientifiques de l'École Normale Supérieure %D 2007 %P 951-983 %V 40 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2007.10.002/ %R 10.1016/j.ansens.2007.10.002 %G fr %F ASENS_2007_4_40_6_951_0
Ratazzi, Nicolas. Borne sur la torsion dans les variétés abéliennes de type CM. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 6, pp. 951-983. doi : 10.1016/j.ansens.2007.10.002. http://archive.numdam.org/articles/10.1016/j.ansens.2007.10.002/
[1] Intersecting a curve with algebraic subgroups of multiplicative groups, Internat. Math. Res. Not. 20 (1999) 1119-1140. | MR | Zbl
, , ,[2] Intersecting curves and algebraic subgroups: conjectures and more results, Trans. Amer. Math. Soc. 358 (2006) 2247-2257. | MR
, , ,[3] The action of the Galois group on the rational cohomology classes of type of abelian varieties, Mat. Sb. (N.S.) 94 (136) (1974) 649-652, 656. | MR | Zbl
,[4] On the Mumford-Tate group of an abelian variety with complex multiplication, J. Algebra 111 (1) (1987) 49-73. | Zbl
,[5] Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin, 1982. | MR | Zbl
, , , ,[6] On the field extension by complex multiplication, Trans. Amer. Math. Soc. 118 (1965) 113-122. | MR | Zbl
,[7] Masser D., Lettre à Daniel Bertrand du 10 novembre 1986.
[8] Small values of the quadratic part of the Néron-Tate height, in: Progr. Math., vol. 12, Birkhäuser, 1981, pp. 213-222. | Zbl
,[9] Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math. 44 (2) (1978) 129-162. | MR | Zbl
,[10] Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math. 124 (1-3) (1996) 437-449. | Zbl
,[11] Abelian varieties, in: Arithmetic Geometry, Storrs, Conn., 1984, Springer, New York, 1984, pp. 103-150. | MR | Zbl
,[12] Hodges classes on abelian varieties of low dimension, Math. Ann. 315 (4) (1999) 711-733. | MR | Zbl
, ,[13] A note of Shimura's paper “Discontinuous groups and abelian varieties”, Math. Ann. 181 (1969) 345-351. | EuDML | Zbl
,[14] Hodge and Weil classes on abelian varieties, in: The Arithmetic and Geometry of Algebraic Cycles, Banff, AB, 1998, NATO Sci. Ser. C Math. Phys. Sci., vol. 548, Kluwer Acad. Publ., Dordrecht, 1998, pp. 83-115. | MR | Zbl
,[15] Arithmetic of algebraic tori, Ann. Math. 74 (1) (1961) 101-139. | MR | Zbl
,[16] Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres, J. reine angew. Math. 506 (1999) 85-116. | MR | Zbl
,[17] ℓ-Adic algebraic monodromy groups cocharacters, and the Mumford-Tate conjecture, J. reine angew. Math. 495 (1998) 187-237. | Zbl
,[18] A common generalization of the conjectures of André-Oort, Manin-Mumford, and Mordell-Lang, Prépublication de 2005 disponible à l'adresse, http://www.math.ethz.ch/~pink/ftp/AOMMML.pdf.
,[19] Interrelations between the Tate and Hodge hypotheses for abelian varieties, Mat. Sb. (N.S.) 85 (127) (1971) 610-620. | MR | Zbl
,[20] Algebraic cycles on abelian varieties of complex multiplication type, Ann. of Math. 88 (2) (1968) 161-180. | MR | Zbl
,[21] Courbes sur une variété abélienne et points de torsion, Invent. Math. 71 (1983) 207-233. | EuDML | MR | Zbl
,[22] Ratazzi N., Intersection de courbes et de sous-groupes, et problèmes de minoration de hauteur dans les variétés abéliennes C.M. À paraître aux Annales de l'Institut Fourier. | EuDML | Numdam | Zbl
[23] Intersection de sous-groupes et de sous-variétés I, Math. Ann. 333 (3) (2005) 525-548. | MR | Zbl
,[24] Problème de Mordell-Lang modulo certaines sous-variétés abéliennes, Int. Math. Res. Not. 35 (2003) 1915-1931. | Zbl
, ,[25] Division fields of abelian varieties with complex multiplication, Mém. Soc. Math. France 2 (1980) 75-94. | EuDML | Numdam | MR | Zbl
,[26] Hodge classes on certain types of abelian varieties, Amer. J. Math. 105 (1983) 523-538. | MR | Zbl
,[27] Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972) 259-331. | EuDML | MR | Zbl
,[28] Représentations ℓ-adiques, in: Kyoto Int. Symposium on Algebraic Number Theory, Japan Soc. for the Promotion of Science, 1977, pp. 177-193. | MR | Zbl
,[29] Lettre à Ken Ribet, Œuvres. Collected papers, vol. IV, Springer-Verlag, Berlin, 2000, 1985-1998. | Zbl
,[30] Résumé des cours au Collège de France de 1984-1985, Œuvres. Collected papers, vol. IV, Springer-Verlag, Berlin, 2000, 1985-1998.
,[31] Abelian ℓ-adic Representations and Elliptic Curves, Research Notes in Mathematics, vol. 7, revised reprint of the 1968 original, AK Peters Ltd., Wellesley, MA, 1998, With the collaboration of Willem Kuyk and John Labute. | MR | Zbl
,[32] Good reduction of abelian varieties, Ann. of Math. 88 (1968) 492-517. | MR | Zbl
, ,[33] Théorie des topos et cohomologie étale des schémas. Tome 3, Springer-Verlag, Berlin, 1973. | MR
[34] Complex Multiplication of Abelian Varieties and Its Applications to Number Theory, Publications of the Mathematical Society of Japan, vol. 6, Mathematical Society of Japan, Tokyo, 1961. | MR | Zbl
, ,[35] Torsion points on abelian varieties of CM-type, Compositio Math. 68 (3) (1988) 241-249. | EuDML | Numdam | MR | Zbl
,[36] Silverman, J.H., Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, vol. 156, 1999. | Zbl
[37] Introduction à la théorie analytique et probabiliste des nombres, Cours Spécialisés, vol. 1, seconde édition, Société Mathématique de France, Paris, 1995. | MR | Zbl
,[38] The intersection of a curve with algebraic subgroups in a product of elliptic curves, Ann. Scuola Norm. Pisa Cl. Sci. Série (V) 2 (2003) 47-75. | EuDML | Numdam | MR | Zbl
,[39] On the rank of CM-type, Nagoya Math. J. 97 (1985) 169-172. | MR | Zbl
,[40] Exponential sums equations and the Schanuel conjecture, J. London Math. Soc. (2) 65 (1) (2002) 27-44. | MR | Zbl
,Cité par Sources :