Arithmetic of division fields

Brumer, Armand; Kramer, Kenneth

doi:10.1090/S0002-9939-2012-11500-X

Arithmetic of division fields
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by Armand Brumer and Kenneth Kramer PDF

Proc. Amer. Math. Soc. 140 (2012), 2981-2995 Request permission

Abstract:

We study the arithmetic of division fields of semistable abelian varieties $A_{/\mathbb {Q}}.$ The Galois group of $\mathbb {Q}(A[2])/\mathbb {Q}$ is analyzed when the conductor of $A$ is odd and squarefree. The irreducible semistable mod 2 representations of small conductor are determined under GRH. These results are used in our paper Paramodular abelian varieties of odd conductor.

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