The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Lior Bary-Soroker, Alexei Entin*, Arno Fehm

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)18199-18253
Number of pages55
JournalInternational Mathematics Research Notices
Volume2023
Issue number21
DOIs
StatePublished - 1 Nov 2023

Funding

FundersFunder number
Shaoul Fund
Israel Science Foundation702/19, 2507/19
Tel Aviv University

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