Galois representations are surjective for almost all Drinfeld modules
Abstract
Abstract This paper advances the results of Duke on the average surjectivity of Galois representations for elliptic curves to the context of Drinfeld modules over function fields. Let be the rational function field over a finite field. We establish that for Drinfeld modules of rank , the ‐adic Galois representation: is surjective for a density 1 set of such modules. The proof utilizes Hilbert irreducibility (over function fields), Drinfeld's uniformization theory and sieve methods.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Polynomial and algebraic computation
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 3
- Publication date
- 1 July 2026
- Language
- EN