The minimal ramification problem for rational function fields over finite fields

Lior Bary-Soroker, Alexei Entin, Arno Fehm

Published 2021-06-16Version 1

We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of number fields, which we establish for abelian, symmetric and alternating groups in many cases.