Une approche polynomiale du théorème de Faltings

We present here an elementary proof of a quantitatively improved version of the Mordell's Conjecture which is now Faltings's Theorem. For the count of the 'large points' of C(K) (see below for the notations) we use Vojta's method which was simplified by Bombieri and then by T. de Diego, G. Rémond. To count the points of small heights of C(K), we use a result of S. David and P. Philippon, allowing to us estimate the number of points of small height of the bigger set C(K¯)∩J(K). To cite this article: B. Farhi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).