2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110156We present here quantitative versions in 1 dimension of Faltings'theorem according to which the set of the K-rational points (where K is a given number field) of an abelian variety A definied over K, which are close (with respect to a v-adic distance on K) to some K-subvariety X of A, but not belonging to X, is finite. We treat more exactly the case where A is an elliptic curve and X is reduced to a point of A and we give (in this case) explicit bounds for the cardinal of the exceptional finite set. We consider also, more generally, instead of only one place v of K, a finite set S of places of K and the distance from the point of A to X taking into account of all places of S.96 pages. Ce texte détaille la note au CRASS référencée: B. Farhi, Un analogue elliptique du théorème de Roth, C. R. Acad. Sci. Paris, Sér. I 341 (2005), p. 275-278Number TheoryCommutative Algebra11J, 11K60text