The Minimal Ramification Problem for Rational Function Fields over Finite Fields-Reference-Cited by-同舟云学术

The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Published:2023-02-06 Issue:21 Volume:2023 Page:18199-18253
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bary-Soroker Lior¹,Entin Alexei¹,Fehm Arno²

Affiliation:

1. Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University , Tel Aviv 69978, Israel

2. Technische Universität Dresden, Fakultät Mathematik , Institut für Algebra, 01062 Dresden, Germany

Abstract

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.

Funder

Israel Science Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2023/21/18199/52943887/rnac370.pdf

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