The Minimal Ramification Problem for Rational Function Fields over Finite Fields
Lior Bary‐Soroker, Alexei Entin, Arno Fehm · International Mathematics Research Notices · 2023
Abstract 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.