Arithmetic of Division Fields

2011/02/22 by Armand Brumer, Brumer, Armand, Kenneth Kramer +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1102.4557

openalex publication_date 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Semistable abelian varieties with small division fields
• Paramodular Abelian Varieties of Odd Conductor
• Galois representations attached to abelian varieties of CM type
• Subfields of nondegenerate tame semiramified division algebras
• Upper bounds for the Euclidean minima of abelian fields of odd prime\n power conductor