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- W4300696119 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 $GSp$ type, i.e. whose Mumford-Tate group is generic (isomorphic to the group of symplectic similitudes) 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 $A$. The result is unconditional for a product of simple abelian varieties with endomorphism ring $Z$ and dimension outside an explicit exceptional set $mathcal{S}={4,10,16,32,...}$. Furthermore, following a strategy of Serre, we also prove that if the Mumford-Tate conjecture is true for some abelian varieties of $GSp$ type, it is then true for a product of such abelian varieties." @default.
- W4300696119 created "2022-10-04" @default.
- W4300696119 creator A5037438552 @default.
- W4300696119 creator A5057147233 @default.
- W4300696119 date "2009-11-29" @default.
- W4300696119 modified "2023-10-16" @default.
- W4300696119 title "Points de torsion sur les varietes abeliennes de type GSp" @default.
- W4300696119 doi "https://doi.org/10.48550/arxiv.0911.5505" @default.
- W4300696119 hasPublicationYear "2009" @default.
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