Borne sur la torsion dans les variétés abéliennes de type CM

Nicolas Ratazzi

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 6, page 951-983
  • ISSN: 0012-9593

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Ratazzi, Nicolas. "Borne sur la torsion dans les variétés abéliennes de type CM." Annales scientifiques de l'École Normale Supérieure 40.6 (2007): 951-983. <http://eudml.org/doc/82731>.

@article{Ratazzi2007,
author = {Ratazzi, Nicolas},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {abelian varieties; torsion points},
language = {fre},
number = {6},
pages = {951-983},
publisher = {Elsevier},
title = {Borne sur la torsion dans les variétés abéliennes de type CM},
url = {http://eudml.org/doc/82731},
volume = {40},
year = {2007},
}

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
PB - Elsevier
VL - 40
IS - 6
SP - 951
EP - 983
LA - fre
KW - abelian varieties; torsion points
UR - http://eudml.org/doc/82731
ER -

References

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  1. [1] Bombieri E., Masser D., Zannier U., Intersecting a curve with algebraic subgroups of multiplicative groups, Internat. Math. Res. Not.20 (1999) 1119-1140. Zbl0938.11031MR1728021
  2. [2] Bombieri E., Masser D., Zannier U., Intersecting curves and algebraic subgroups: conjectures and more results, Trans. Amer. Math. Soc.358 (2006) 2247-2257. Zbl1161.11025MR2197442
  3. [3] Borovoĭ M.V., The action of the Galois group on the rational cohomology classes of type ( p , p ) of abelian varieties, Mat. Sb. (N.S.)94 (136) (1974) 649-652, 656. Zbl0326.14013MR352101
  4. [4] Dodson B., On the Mumford–Tate group of an abelian variety with complex multiplication, J. Algebra111 (1) (1987) 49-73. Zbl0637.14022
  5. [5] Deligne P., Milne J.S., Ogus A., Shih K.-Y., Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin, 1982. Zbl0465.00010MR654325
  6. [6] Kubota T., On the field extension by complex multiplication, Trans. Amer. Math. Soc.118 (1965) 113-122. Zbl0146.27902MR190144
  7. [7] Masser D., Lettre à Daniel Bertrand du 10 novembre 1986. 
  8. [8] Masser D., Small values of the quadratic part of the Néron–Tate height, in: Progr. Math., vol. 12, Birkhäuser, 1981, pp. 213-222. Zbl0455.14024
  9. [9] Mazur B., Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math.44 (2) (1978) 129-162. Zbl0386.14009MR482230
  10. [10] Merel L., Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math.124 (1–3) (1996) 437-449. Zbl0936.11037
  11. [11] Milne J.S., Abelian varieties, in: Arithmetic Geometry, Storrs, Conn., 1984, Springer, New York, 1984, pp. 103-150. Zbl0604.14028MR861974
  12. [12] Moonen B., Zarhin Y., Hodges classes on abelian varieties of low dimension, Math. Ann.315 (4) (1999) 711-733. Zbl0947.14005MR1731466
  13. [13] Mumford D., A note of Shimura's paper “Discontinuous groups and abelian varieties”, Math. Ann.181 (1969) 345-351. Zbl0169.23301
  14. [14] Murty V.K., 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. Zbl1028.14016MR1744944
  15. [15] Ono T., Arithmetic of algebraic tori, Ann. Math.74 (1) (1961) 101-139. Zbl0119.27801MR124326
  16. [16] Parent P., Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres, J. reine angew. Math.506 (1999) 85-116. Zbl0919.11040MR1665681
  17. [17] Pink R., ℓ-Adic algebraic monodromy groups cocharacters, and the Mumford–Tate conjecture, J. reine angew. Math.495 (1998) 187-237. Zbl0920.14006
  18. [18] Pink R., 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. Zbl1200.11041
  19. [19] Pjateckiĭ-Šapiro I.I., Interrelations between the Tate and Hodge hypotheses for abelian varieties, Mat. Sb. (N.S.)85 (127) (1971) 610-620. Zbl0229.14014MR294352
  20. [20] Pohlmann H., Algebraic cycles on abelian varieties of complex multiplication type, Ann. of Math.88 (2) (1968) 161-180. Zbl0201.23201MR228500
  21. [21] Raynaud M., Courbes sur une variété abélienne et points de torsion, Invent. Math.71 (1983) 207-233. Zbl0564.14020MR688265
  22. [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. 
  23. [23] Rémond G., Intersection de sous-groupes et de sous-variétés I, Math. Ann.333 (3) (2005) 525-548. Zbl1088.11047MR2198798
  24. [24] Rémond G., Viada E., Problème de Mordell–Lang modulo certaines sous-variétés abéliennes, Int. Math. Res. Not.35 (2003) 1915-1931. Zbl1072.11038
  25. [25] Ribet K.A., Division fields of abelian varieties with complex multiplication, Mém. Soc. Math. France2 (1980) 75-94. Zbl0452.14009MR608640
  26. [26] Ribet K.A., Hodge classes on certain types of abelian varieties, Amer. J. Math.105 (1983) 523-538. Zbl0586.14003MR701568
  27. [27] Serre J.-P., Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15 (1972) 259-331. Zbl0235.14012MR387283
  28. [28] Serre J.-P., Représentations ℓ-adiques, in: Kyoto Int. Symposium on Algebraic Number Theory, Japan Soc. for the Promotion of Science, 1977, pp. 177-193. Zbl0406.14015MR476753
  29. [29] Serre J.-P., Lettre à Ken Ribet, Œuvres. Collected papers, vol. IV, Springer-Verlag, Berlin, 2000, 1985–1998. 
  30. [30] Serre J.-P., Résumé des cours au Collège de France de 1984–1985, Œuvres. Collected papers, vol. IV, Springer-Verlag, Berlin, 2000, 1985–1998. 
  31. [31] Serre J.-P., 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. Zbl0902.14016MR263823
  32. [32] Serre J.-P., Tate J., Good reduction of abelian varieties, Ann. of Math.88 (1968) 492-517. Zbl0172.46101MR236190
  33. [33] Théorie des topos et cohomologie étale des schémas. Tome 3, Springer-Verlag, Berlin, 1973. MR354654
  34. [34] Shimura G., Taniyama Y., 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. Zbl0112.03502MR125113
  35. [35] Silverberg A., Torsion points on abelian varieties of CM-type, Compositio Math.68 (3) (1988) 241-249. Zbl0683.14002MR971328
  36. [36] Silverman, J.H., Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, vol. 156, 1999. Zbl0911.14015
  37. [37] Tenenbaum G., Introduction à la théorie analytique et probabiliste des nombres, Cours Spécialisés, vol. 1, seconde édition, Société Mathématique de France, Paris, 1995. Zbl0880.11001MR1366197
  38. [38] Viada E., 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. Zbl1170.11314MR1990974
  39. [39] Yanai H., On the rank of CM-type, Nagoya Math. J.97 (1985) 169-172. Zbl0557.14026MR781495
  40. [40] Zilber B., Exponential sums equations and the Schanuel conjecture, J. London Math. Soc. (2)65 (1) (2002) 27-44. Zbl1030.11073MR1875133

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