The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

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.

Details

Original languageEnglish
Pages (from-to)18199-18253
Number of pages55
JournalInternational mathematics research notices
Volume2023
Issue number21
Publication statusPublished - Nov 2023
Peer-reviewedYes

External IDs

Mendeley addbd8af-5744-36e6-8427-9775115c8592
Scopus 85178060311

Keywords

Keywords

  • Primitive permutation-groups, Alternating group coverings, Affine line, Irreducible values, Polynomials, Extensions, Conjecture, Primes, Number

Library keywords