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arXiv · 1505.05620

Torsion pour les varietes abeliennes de type I et II

Marc Hindry·Nicolas Ratazzi
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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]. When A is isogenous to a product of simple abelian varieties of type I or II in Albert classification and is "fully of Lefschetz type", i.e. whose Mumford-Tate group is the group of symplectic similitudes commuting with endomorphisms and which satisfy the Mumford-Tate conjecture, we compute the optimal exponent for this bound in terms of the dimensions of the abelian subvarieties of A and their rings of endomorphisms. The result is unconditional for a product of simple abelian varieties of type I or II with odd relative dimension. Extending work of Serre, Pink and Hall, we also prove that the Mumford-Tate conjecture is true for a few new cases for such abelian varieties.

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BibTeXRIS

Marc Hindry, Nicolas Ratazzi. 2016-12-01. Torsion pour les varietes abeliennes de type I et II. https://doi.org/10.2140/ant.2016.10.1845

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