Journal of the Ramanujan Mathematical Society

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Torsion Dans Un Produit De Courbes Elliptiques


Affiliations
1 Institut De Mathematiques De Jussieu Universite Paris 7 Denis Diderot, Case Postale 7012, 175, Rue De Chevaleret F-75013, Paris, France
2 Universite Paris-Sud, Departement De Mathematiques, Batiment 425, 91405 Orsay Cedex, France
     

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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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  • Torsion Dans Un Produit De Courbes Elliptiques

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Authors

Marc Hindry
Institut De Mathematiques De Jussieu Universite Paris 7 Denis Diderot, Case Postale 7012, 175, Rue De Chevaleret F-75013, Paris, France
Nicolas Ratazzi
Universite Paris-Sud, Departement De Mathematiques, Batiment 425, 91405 Orsay Cedex, France

Abstract


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.