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.
Cite
@article{arxiv.1102.4557,
title = {Arithmetic of Division Fields},
author = {Armand Brumer and Kenneth Kramer},
journal= {arXiv preprint arXiv:1102.4557},
year = {2011}
}