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Autour du Théorème du Sous-Groupe Algébrique

Published online by Cambridge University Press:  20 November 2018

Damien Roy  and
Michel Waldschmidt
Damien Roy
Affiliation:
McGill University Department of Mathematics 805, rue Sherbrooke Ouest Montréal, Québec H3A 2K6
Michel Waldschmidt
Affiliation:
Université P. et M. Curie (Paris VI) Problèmes Diophantiens, URA 763 du C.N.R.S. Institut Henri Poincaré II, rue P. et M. Curie 75231 Paris Cedex 05 France
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Résumé

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A known consequence of the theorem of the algebraic subgroup is a lower bound for the rank of matrices whose entries are linear combinations, with algebraic coefficients, of logarithms of algebraic numbers. We extend this kind of result to commutative algebraic groups.

Keywords

11J81
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 3 , 01 September 1993 , pp. 358 - 367
Copyright
Copyright © Canadian Mathematical Society 1993

References

[Bl] Bertrand, D., Endomorphismes de groupes algébriques; applications arithmétiques, Approximations Diophantiennes et Nombres Transcendants, (éd. D. Bertrand et M. Waldschmidt), Proc. Conf. Luminy 1982, Progress in Math. 31, Birkhauser (1983), 1-45.Google Scholar
[B2] , Lemmes de zéros et nombres transcendants, Sém. Bourbaki 38ème année, Nov. 85, no. 82 ; Astérisque 145-146(1987), 21–44.Google Scholar
[Hindry, H. M., Autour d'une conjecture de Serge Lang, Invent, math. 94(1988), 575–603.Google Scholar
[L] Lang, S., Fundamentals of Diophantine Geometry, Springer Verlag, 1983.Google Scholar
[M] Masser, D., Small values of the quadratic part of the Néron-Tate height on an abelian variety, Compositio Mathematica 53(1984), 153–170.Google Scholar
[RI] Roy, D., Transcendance et questions de répartition dans les groupes algébriques, Approximations Diophantiennes et Nombres Transcendants, (éd. P. Philippon),Proc. Conf. Luminy 1990,W. de Gruyter(1992), 249–274.Google Scholar
[R2] Roy, D., Matrices whose coefficients are linear forms in logarithms, J. Number Theory 41(1992), 22–417.Google Scholar
[SD] Swinnerton-Dyer, H. P. F., Analytic Theory of Abelian Varieties, London Math. Soc. Lect. Note Ser. 14, Cambridge Univ. Press 1974.Google Scholar
[Wl] Waldschmidt, M., On the transcendence methods of Gelfond and Schneider in several variables, New Advances in Transcendence Theory, (éd. A. Baker), Cambridge Univ. Press. 1988, Chap. 24, 375–398.Google Scholar
[W2] Waldschmidt, M., Dependence of logarithms of algebraic points, Number Theory, Vol. II, Diophantine and Algebraic, Coll. Math. Soc. J. Bolyai 51, North Holland (1987), 1013–1035.Google Scholar