On the Frobenius fields of abelian varieties over number fields
Abstract
Let A be a non-CM simple abelian variety over a number field K.For a place v of K where A has good reduction, let F.A; v/ denote the Frobenius field generated by the corresponding Frobenius eigenvalues.If 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.Moreover, assuming the GRH, we give a power saving upper bound for the number of such places.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Tensor decomposition and applications
Publication details
- Journal / source
- Algebra & Number Theory
- Volume
- 20
- Issue
- 3
- Pages
- 577–601
- Publication date
- 24 March 2026
- Language
- EN