On the Frobenius fields of abelian varieties over number fields

2024/02/06 by Burungale, Ashay A., Hida, Haruzo, Lai, Shilin
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.07935

Abstract

Let A be a non-CM simple abelian variety over a number field K. For a place v of K such that A has good reduction at v, let F(A,v) denote the Frobenius field generated by the corresponding Frobenius eigenvalues. Assuming A has connected monodromy groups, we show that the set of places v such that F(A,v) is isomorphic to a fixed number field has upper Dirichlet density zero. Assuming the GRH, we give a power saving upper bound for the number of such places.

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