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Logarithmes des points rationnels des variétés abéliennes

  • Vincent Bosser (a1) and Éric Gaudron (a2)
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Les auteurs ont bénéficié du soutien du projet ANR Gardio 14-CE25-0015.

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[Au] Autissier, P., Un lemme matriciel effectif . Math. Z. 273(2013), 355361. https://doi.org/10.1007/s00209-012-1008-x.
[BW] Baker, A. and Wüstholz, G., Logarithmic forms and group varieties . J. Reine Angew. Math. 442(1993), 1962. https://doi.org/10.1515/crll.1993.442.19.
[Ba] Banaszczyk, W., New bounds in some transference theorems in the geometry of numbers . Math. Ann. 296(1993), 625635. https://doi.org/10.1007/BF01445125.
[Be] Bertrand, D., Minimal heights and polarizations on group varieties . Duke Math. J. 80(1995), 223250. https://doi.org/10.1215/S0012-7094-95-08009-0.
[BP] Bertrand, D. and Philippon, P., Sous-groupes algébriques de groupes algébriques commutatifs . Illinois J. Math. 32(1988), 263280. https://projecteuclid.org/euclid.ijm/1255989130.
[Bo1] Bost, J.-B., Périodes et isogénies des variétés abéliennes sur les corps de nombres (d’après D. Masser et G. Wüstholz). Astérisque (1996), no. 237, 115–161. http://www.numdam.org/item?id=SB_1994-1995_37_115_0.
[Bo2] Bost, J.-B., Intrinsic heights of stable varieties and abelian varieties . Duke Math. J. 82(1996), 2170. https://doi.org/10.1215/S0012-7094-96-08202-2.
[CW] Cijsouw, P. and Waldschmidt, M., Linear forms and simultaneous approximations . Compositio Math. 34(1977), 173197. http://www.numdam.org/item?id=CM_1977_34_2_173_0.
[Da] David, S., Approximation diophantienne sur les variétés abéliennes. École doctorale de Géométrie diophantienne. Rennes (France), 15–26 juin 2009.
[Ga1] Gaudron, É., Formes linéaires de logarithmes effectives sur les variétés abéliennes . Ann. Sci. École Norm. Sup. 39(2006), 699773. https://doi.org/10.1016/j.ansens.2006.09.001.
[Ga2] Gaudron, É., Pentes des fibrés vectoriels adéliques sur un corps global . Rend. Sem. Mat. Univ. Padova 119(2008), 2195. https://doi.org/10.4171/RSMUP/119-2.
[Ga3] Gaudron, É., Minorations simultanées de formes linéaires de logarithmes de nombres algébriques . Bull. Soc. Math. Fr. 142(2014), 162. https://doi.org/10.24033/bsmf.2658.
[Ga4] Gaudron, É., Lower bound for the Néron–Tate height (with V. Bosser). In: Oberwolfach Reports, 21. 2016, p. 22–24.
[GR1] Gaudron, É. and Rémond, G., Minima, pentes et algèbre tensorielle . Israel J. Math. 195(2013), 565591. https://doi.org/10.1007/s11856-012-0109-x.
[GR2] Gaudron, É. and Rémond, G., Théorème des périodes et degrés minimaux disogénies . Commen. Math. Helv. 89(2014), 343403. https://doi.org/10.4171/CMH/322.
[GR3] Gaudron, É. and Rémond, G., Polarisations et isogénies . Duke Math. J. 163(2014), 20572108. https://doi.org/10.1215/00127094-2782528.
[GS] Gillet, H. and Soulé, C., An arithmetic Riemann-Roch theorem . Invent. Math. 110(1992), 473543. https://doi.org/10.1007/BF01231343.
[Ma] Masser, D., Small values of heights on families of abelian varieties. In: Diophantine approximation and transcendence theory. Lecture Notes in Math., 1290, Springer, Berlin, 1987, pp. 109–148. https://doi.org/10.1007/BFb0078706.
[MaWü] Masser, D. and Wüstholz, G., Periods and minimal abelian subvarieties . Ann. of Math. 137(1993), 407458. https://doi.org/10.2307/2946542.
[MiWa] Mignotte, M. and Waldschmidt, M., Linear forms in two logarithms and Schneider’s method. II . Acta Arith. 53(1989), 251287. https://doi.org/10.4064/aa-53-3-251-287.
[MH] Milnor, J. and Husemoller, D., Symmetric bilinear forms. volume 73 de Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, 1973.
[Na] Nakamaye, M., Multiplicity estimates on commutative algebraic groups . J. Reine Angew. Math. 607(2007), 217235. https://doi.org/10.1515/CRELLE.2007.049.
[Pe] Pellarin, F., Sur la distance d’un point algébrique à l’origine dans les variétés abéliennes . J. Number Theory 88(2001), 241262. https://doi.org/10.1006/jnth.2000.2612.
[PW] Philippon, P. and Waldschmidt, M., Formes linéaires de logarithmes sur les groupes algébriques commutatifs . Illinois J. Math. 32(1988), 281314. https://projecteuclid.org/euclid.ijm/1255989131.
[Ré1] Rémond, G., Conjectures uniformes sur les variétés abéliennes . Quarterly J. Math. 69(2018), 459486. https://doi.org/10.1093/qmath/hax042.
[Ré2] Rémond, G., Degré de définition des endomorphismes d’une variété abélienne. Prépublication 2017. https://www-fourier.ujf-grenoble.fr/∼remond/4441.pdf.
[Si] Silverberg, A., Fields of definition for homomorphisms of abelian varieties . J. Pure Appl. Algebra 77(1992), 253262. https://doi.org/10.1016/0022-4049(92)90141-2.
[Wi] Winckler, B., Problème de Lehmer sur les courbes elliptiques à multiplications complexes . Acta Arith. 182(2018), 347396. https://doi.org/10.4064/aa170404-5-11.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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