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arXiv · 2309.00531

On abelian varieties whose torsion is not self-dual

Sarah Frei·Katrina Honigs·John Voight
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Abstract

We construct infinitely many abelian surfaces A defined over the rational numbers such that, for a prime ell <= 7, the ell-torsion subgroup of A is not isomorphic as a Galois module to the ell-torsion subgroup of its dual. We do this by explicitly analyzing the action of the Galois group on the ell-adic Tate module and its reduction modulo ell.

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Sarah Frei, Katrina Honigs, John Voight. 2023-09-01. On abelian varieties whose torsion is not self-dual. https://arxiv.org/abs/2309.00531

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