Approximation diophantienne sur une courbe elliptique

Details Approximation diophantienne sur une courbe elliptique Approximation diophantienne sur une courbe elliptique

2006-03-12

arxiv.org/abs/math/0603278v2

Mathematics

Number Theory

96 pages. Ce texte d\'etaille la note au CRASS r\'ef\'erenc\'ee: B. Farhi, Un analogue elliptique du th\'eor\`eme de Roth, C.

Scientific paper

We 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.

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