Borne sur la torsion dans les variétés abéliennes de type C.M

Details Borne sur la torsion dans les variétés abéliennes de type C.M Borne sur la torsion dans les variétés abéliennes de type C.M

2005-02-09

arxiv.org/abs/math/0502185v3

Mathematics

Number Theory

30 pages, final version, accepted for publication in Annales Scientifiques de l'Ecole Normale Superieure

Scientific paper

Let 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 \gamma in the inequality Card(A(F)_{tors})<< [F:K]^{\gamma} 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 R\'emond generalising the Manin-Mumford conjecture.

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