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Comptes Rendus Mathématique
Volume 334, n° 4
pages 267-271 (2002)
Doi : S1631-073X(02)02240-9
Received : 27 November 2001 ;  accepted : 10 December 2001
A subspace theorem approach to integral points on curves
Points entiers sur les courbes et théorème des sous-espaces
 

Pietro Corvaja a , Umberto Zannier b
a Dip. di Matematica e Informatica, Via delle Scienze, 33100 Udine, Italy 
b Ist. Univ. Arch.-D.C.A., S. Croce, 191, 30135 Venezia, Italy 

Note presented by Enrico Bombieri

Abstract

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. To cite this article: P. Corvaja, U. Zannier, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 267-271.

The full text of this article is available in PDF format.
Résumé

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. Pour citer cet article : P. Corvaja, U. Zannier, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 267-271.

The full text of this article is available in PDF format.


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