On abelian varieties whose torsion is not self-dual
Number Theory
2025-09-18 v4 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2309.00531,
title = {On abelian varieties whose torsion is not self-dual},
author = {Sarah Frei and Katrina Honigs and John Voight},
journal= {arXiv preprint arXiv:2309.00531},
year = {2025}
}
Comments
16 pages. v4: elaboration of some proofs, further edits suggested by referees