Torsion dans un produit de courbes elliptiques

Details Torsion dans un produit de courbes elliptiques Torsion dans un produit de courbes elliptiques

2008-04-18

arxiv.org/abs/0804.3031v1

Mathematics

Number Theory

23 pages

Scientific paper

Let $A$ be an abelian variety defined over a number field $K$, the number of torsion points rational over a finite extension $L$ is bounded polynomially in terms of the degree $[L:K]$. We formulate a question suggesting the optimal exponent for this bound in terms of the dimension of the Mumford-Tate groups of the abelian subvarieties of $A$; we study the behaviour under product and then give a positive answer to our question when $A$ is the product of elliptic curves.

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