English

Arithmetic of Division Fields

Number Theory 2011-02-23 v1

Abstract

We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2 representations of small conductor are determined under GRH. These results are used in "Paramodular abelian varieties of odd conductor," arXiv:1004.4699.

Keywords

Cite

@article{arxiv.1102.4557,
  title  = {Arithmetic of Division Fields},
  author = {Armand Brumer and Kenneth Kramer},
  journal= {arXiv preprint arXiv:1102.4557},
  year   = {2011}
}
R2 v1 2026-06-21T17:30:07.656Z