SÉMINAIRE DE THÉORIE DES NOMBRES 2000-2001 Le Vendredi à 15 heures 30 en Salle de Conférence Organisateur : Arnaud Jehanne

Yuri Bilu
(Université Bordeaux 1)
Les cas effectifs du théorème diophantien de Siegel
RÉSUMÉ

Siegel (1929) proved that an affine curve (defined over rationals) has only finitely many integral points, unless it is of genus 0 and has at most 2 points at infinity. Siegel's argument was non-effective (did not supply a bound for size of the integral points). In sixties, A. Baker developed a new method which allowed him to obtain effective versions of Siegel's theorem in many special cases. I will discuss various cases when Siegel's theorem is effective, and, if time permits, will outline a proof of a recent result: Effective Siegel's theorem for modular curves.
The talk will be given in French.
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\title{Les cas effectifs du th\'eor\eme diophantien de Siegel} \author{Yuri Bilu} \date{Bordeaux, 27.10.2000} \begin{document} \maketitle \noindent Siegel (1929) proved that an affine curve (defined over rationals) has only finitely many integral points, unless it is of genus~$0$ and has at most~$2$ points at infinity. Siegel's argument was non-effective (did not supply a bound for size of the integral points). In sixties, A.~Baker developed a new method which allowed him to obtain effective versions of Siegel's theorem in many special cases. I will discuss various cases when Siegel's theorem is effective, and, if time permits, will outline a proof of a recent result: {\bf effective Siegel's theorem for modular curves.} The talk will be given in `French''. \end{document}