The minimal ramification problem for rational function fields over finite fields

2021/06/16 by Lior Bary‐Soroker, Bary-Soroker, Lior, Alexei Entin +3
Computer Science · Mathematics · #11R32 #11R58 #11S15 #12F12 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2106.09126

openalex publication_date 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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