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.
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