Galois representations attached to abelian varieties of CM type

2015/06/15 by Davide Lombardo, Lombardo, Davide
Computer Science · Mathematics · #11F80 #11G10 #14K22 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1506.04734

openalex publication_date 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a number field, A/K be an absolutely simple abelian variety of CM type, and ℓ be a prime number. We give explicit bounds on the degree over K of the division fields K(A[ℓⁿ]), and when A is an elliptic curve we also describe the full Galois group of K(A_tors)/K. This makes explicit previous results of Serre and Ribet, and strengthens a theorem of Banaszak, Gajda and Krasoń. Our bounds are especially sharp in case the CM type of A is nondegenerate.

Citations

• Good Reduction of Abelian Varieties

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