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

Nicolas Ratazzi
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Abstract

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 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.

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Nicolas Ratazzi. 2007-10-15. Borne sur la torsion dans les variétés abéliennes de type C.M. https://arxiv.org/abs/math/0502185

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