On abelian varieties whose torsion is not self-dual
Sarah Frei, Katrina Honigs, John Voight
Published: 2023/9/1
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.