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arXiv · 1901.00118

Approximation forte sur un produit de vari\'et\'es ab\'eliennes \'epoint\'e en des points de torsion

Yongqi Liang
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Abstract

Consider strong approximation for algebraic varieties defined over a number field $k$. Let $S$ be a finite set of places of $k$ containing all archimedean places. Let $E$ be an elliptic curve of positive Mordell-Weil rank and let $A$ be an abelian variety of positive dimension and of finite Mordell-Weil group. For an arbitrary finite set $\mathfrak{T}$ of torsion points of $E\times A$, denote by $X$ its complement. Supposing the finiteness of $Sha(E\times A)$, we prove that $X$ satisfies strong approximation with Brauer-Manin obstruction off $S$ if and only if the projection of $\mathfrak{T}$ to $A$ contains no $k$-rational points.

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Yongqi Liang. 2019-01-01. Approximation forte sur un produit de vari\'et\'es ab\'eliennes \'epoint\'e en des points de torsion. https://arxiv.org/abs/1901.00118

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