Small values of the quadratic part of the Néron-Tate height on an abelian variety

D. W. Masser

Compositio Mathematica (1984)

  • Volume: 53, Issue: 2, page 153-170
  • ISSN: 0010-437X

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Masser, D. W.. "Small values of the quadratic part of the Néron-Tate height on an abelian variety." Compositio Mathematica 53.2 (1984): 153-170. <http://eudml.org/doc/89682>.

@article{Masser1984,
author = {Masser, D. W.},
journal = {Compositio Mathematica},
keywords = {Néron-Tate height; field of definition; transcendental numbers},
language = {eng},
number = {2},
pages = {153-170},
publisher = {Martinus Nijhoff Publishers},
title = {Small values of the quadratic part of the Néron-Tate height on an abelian variety},
url = {http://eudml.org/doc/89682},
volume = {53},
year = {1984},
}

TY - JOUR
AU - Masser, D. W.
TI - Small values of the quadratic part of the Néron-Tate height on an abelian variety
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 53
IS - 2
SP - 153
EP - 170
LA - eng
KW - Néron-Tate height; field of definition; transcendental numbers
UR - http://eudml.org/doc/89682
ER -

References

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  1. [1] M. Anderson and D.W. Masser: Lower bounds for heights on elliptic curves. Math. Zeit.174 (1980) 23-34. Zbl0421.14006MR591611
  2. [2] A.O. Gelfond: Transcendental and algebraic numbers. New York: Dover (1960). Zbl0090.26103MR111736
  3. [3] E.R. Kolchin: Algebraic groups and algebraic dependence. Amer. J. Math.90 (1968) 1151-1164. Zbl0169.36701MR240106
  4. [4] S. Lang: Les formes bilinéaires de Néron et Tate. Sém. Bourbaki, 16e année (1963/4), No. 274. Zbl0138.42101MR176984
  5. [5] M. Laurent: Minoration de la hauteur de Néron-Tate, Thèse d'Etat, Université de Paris VI (1982). MR729165
  6. [6] D.W. Masser: Division fields of elliptic functions, Bull. London Math. Soc.9 (1977) 49-53. Zbl0356.12018MR444572
  7. [7] D.W. Masser: Small values of the quadratic part of the Néron-Tate height, Progress in Math. Vol. 12. Boston, Basel, Stuttgart: Birkhäuser (1981) pp. 213-222. Zbl0455.14024
  8. [8] D.W. Masser and G. Wüstholz: Fields of large transcendence degree generated by values of elliptic functions. Invent Math.72 (1983) 407-464. Zbl0516.10027MR704399
  9. [9] P. Philippon: Indépendance algébrique de valeurs de fonctions exponentielles p-adiques. J. reine angew. Math.329 (1981) 42-51. Zbl0459.10024MR636442
  10. [10] A. Schinzel and H. Zassenhaus: A refinement of two theorems of Kronecker. Michigan Math. J.12 (1965) 81-85. Zbl0128.03402MR175882
  11. [11] J.-P. Serre: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Invent. Math.15 (1972) 259-331. Zbl0235.14012MR387283
  12. [12] J.-P. Serre: Quelques applications du théorème de densité de Chebotarev. Publ. Math. I.H.E.S. 54 (1981) 323-401. Zbl0496.12011MR644559
  13. [13] C.L. Stewart: Algebraic integers whose conjugates lie near the unit circle. Bull. Soc. Math. France106 (1978) 169-176. Zbl0396.12002MR507748
  14. [14] M. Waldschmidt: Nombres transcendants et groupes algébriques. Astérisque 69-70 (1979). Zbl0428.10017MR570648
  15. [15] D.W. Masser and G. Wüstholz: Zero estimates on group varieties I. Invent. Math.64 (1981) 489-516. Zbl0467.10025MR632987
  16. [16] F.A. Bogomolov: Sur l'algébricité des représentations l-adiques. C.R. Acad. Sci. Paris290A (1980) 701-703. Zbl0457.14020

Citations in EuDML Documents

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  1. Alice Silverberg, Torsion points on abelian varieties of CM-type
  2. Sinnou David, Fonctions thêta et points de torsion des variétés abéliennes
  3. Nicolas Ratazzi, Intersection de courbes et de sous-groupes et problèmes de minoration de hauteur dans les variétés abéliennes C.M.
  4. Daniel Bertrand, Lemmes de zéros et nombres transcendants
  5. Jean-Benoît Bost, Périodes et isogénies des variétés abéliennes sur les corps de nombres
  6. M. L. Brown, The density of rational and integral points on algebraic varieties
  7. D. Bertrand, M. Emsalem, F. Gramain, M. Huttner, M. Langevin, M. Laurent, M. Mignotte, J.-C. Moreau, P. Philippon, E. Reyssat, M. Waldschmidt, Les nombres transcendants

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