Let K be a number field, A/K be an absolutely simple abelian variety of CM type, and be a prime number. We give explicit bounds on the degree over K of the division fields K(A[^n]), 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 [17] and Ribet [14], and strengthens a theorem of Banaszak, Gajda and Krasoń [2]. Our bounds are especially sharp when the CM type of A is nondegenerate.
Galois representations attached to abelian varieties of CM type
Davide Lombardo
Primo
2017-01-01
Abstract
Let K be a number field, A/K be an absolutely simple abelian variety of CM type, and be a prime number. We give explicit bounds on the degree over K of the division fields K(A[^n]), 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 [17] and Ribet [14], and strengthens a theorem of Banaszak, Gajda and Krasoń [2]. Our bounds are especially sharp when the CM type of A is nondegenerate.File in questo prodotto:
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