[Points entiers sur les courbes et théorème des sous-espaces]
Nous donnons une nouvelle démonstration du théorème de Siegel sur les points entiers des courbes, qui repose sur le théorème des sous-espaces de Schmidt. Notre méthode n'utilise pas le plongement d'une courbe dans sa jacobienne, évitant ainsi l'utilisation de résultats sur l'arithmétique des variétés abéliennes.
We present a proof of Siegel's theorem on integral points on affine curves, through the Schmidt subspace theorem, rather than Roth's theorem. This approach allows one to work only on curves, avoiding the embedding into Jacobians and the subsequent use of tools from the arithmetic of Abelian varieties.
Accepté le :
Publié le :
@article{CRMATH_2002__334_4_267_0,
author = {Corvaja, Pietro and Zannier, Umberto},
title = {A subspace theorem approach to integral points on curves},
journal = {Comptes Rendus. Math\'ematique},
pages = {267--271},
publisher = {Elsevier},
volume = {334},
number = {4},
year = {2002},
doi = {10.1016/S1631-073X(02)02240-9},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02240-9/}
}
TY - JOUR AU - Corvaja, Pietro AU - Zannier, Umberto TI - A subspace theorem approach to integral points on curves JO - Comptes Rendus. Mathématique PY - 2002 SP - 267 EP - 271 VL - 334 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02240-9/ DO - 10.1016/S1631-073X(02)02240-9 LA - en ID - CRMATH_2002__334_4_267_0 ER -
%0 Journal Article %A Corvaja, Pietro %A Zannier, Umberto %T A subspace theorem approach to integral points on curves %J Comptes Rendus. Mathématique %D 2002 %P 267-271 %V 334 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02240-9/ %R 10.1016/S1631-073X(02)02240-9 %G en %F CRMATH_2002__334_4_267_0
Corvaja, Pietro; Zannier, Umberto. A subspace theorem approach to integral points on curves. Comptes Rendus. Mathématique, Tome 334 (2002) no. 4, pp. 267-271. doi : 10.1016/S1631-073X(02)02240-9. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02240-9/
[1] An improvement of the quantitative subspace theorem, Compositio Math., Volume 101 (1996), pp. 225-311
[2] Endlichkeitssätzes für abelsche Varietäten über Zahlkörpern, Invent. Math., Volume 73 (1983), pp. 349-366
[3] Riemann Surfaces, Springer-Verlag, 1981
[4] Diophantine Geometry, Springer-Verlag, 2000
[5] Fundamentals of Diophantine Geometry, Springer-Verlag, 1982
[6] The quantitative subspace theorem for number fields, Compositio Math., Volume 82 (1992), pp. 245-273
[7] Diophantine Approximation, Lecture Notes in Math., 785, Springer-Verlag, 1987
[8] Diophantine Approximations and Diophantine Equations, Lecture Notes in Math., 1467, Springer-Verlag, 1991
[9] Lectures on the Mordell–Weil Theorem, Vieweg, 1989
[10] Über einige Anwendungen diophantischer Approximationen, Abh. Pr. Akad. Wiss., Volume 1 (1929) (Ges. Abh., I, 209–266)
[11] P. Vojta, Diophantine Approximations and Value Distribution theory, Lecture Notes in Math. 1239, Springer-Verlag
Cité par Sources :
