2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139949Let A be an abelian variety of dimension g defined over a number field K. We study the size of the torsion group A(F)_{tors} where F/K is a finite extension and more precisely we study the possible exponent γin the inequality Card(A(F)_{tors})<< [F:K]^γ when F is any extension of K. In the C.M. case we give an exact formula for the best possible exponent in terms of the characters of the Mumford-Tate group--a torus in this case--and discuss briefly the general case. Finally we give applications of this result in direction of a conjecture of Rémond generalising the Manin-Mumford conjecture.30 pages, final version, accepted for publication in Annales Scientifiques de l'Ecole Normale SuperieureNumber TheoryAlgebraic Geometry1G10; 11G15; 14K15; 11F80text