Comptes Rendus
no. 4
A subspace theorem approach to integral points on curves
[Points entiers sur les courbes et théorème des sous-espaces]
Pietro Corvaja1 ; Umberto Zannier2
1 Dip. di Matematica e Informatica, Via delle Scienze, 33100 Udine, Italy
2 Ist. Univ. Arch.-D.C.A., S. Croce, 191, 30135 Venezia, Italy
Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 267-271.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02240-9
Pietro Corvaja 1 ; Umberto Zannier 2

1 Dip. di Matematica e Informatica, Via delle Scienze, 33100 Udine, Italy
2 Ist. Univ. Arch.-D.C.A., S. Croce, 191, 30135 Venezia, Italy 
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Pietro Corvaja; Umberto Zannier. A subspace theorem approach to integral points on curves. Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 267-271. doi : 10.1016/S1631-073X(02)02240-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02240-9/

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[6] H.P. Schlickewei The quantitative subspace theorem for number fields, Compositio Math., Volume 82 (1992), pp. 245-273

[7] W.M. Schmidt Diophantine Approximation, Lecture Notes in Math., 785, Springer-Verlag, 1987

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