Drinfeld modules, Frobenius endomorphisms, and CM-liftings

Abstract

We give a global description of the Frobenius elements in the division fields of Drinfeld modules of rank $2$. We apply this description to derive a criterion for the splitting modulo primes of a class of non-solvable polynomials, and to study the frequency with which the reductions of Drinfeld modules have small endomorphism rings. We also generalize some of these results to higher rank Drinfeld modules and prove CM-lifting theorems for Drinfeld modules.

arXiv comment30 pages. Some of the main results are extended to Drinfeld modules of arbitrary rank. To appear in IMRN

References in corpus (1)

• Drinfeld modules with maximal Galois action on their torsion points