English

The minimal ramification problem for rational function fields over finite fields

Number Theory 2022-12-26 v3

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.

Keywords

Cite

@article{arxiv.2106.09126,
  title  = {The minimal ramification problem for rational function fields over finite fields},
  author = {Lior Bary-Soroker and Alexei Entin and Arno Fehm},
  journal= {arXiv preprint arXiv:2106.09126},
  year   = {2022}
}

Comments

v3: minor changes

R2 v1 2026-06-24T03:17:27.503Z