The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Lior Bary-Soroker; Alexei Entin; Arno Fehm

doi:https://doi.org/10.1093/imrn/rnac370

The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Lior Bary-Soroker, Alexei Entin, Arno Fehm

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	18199-18253
Number of pages	55
Journal	International Mathematics Research Notices
Volume	2023
Issue number	21
DOIs	https://doi.org/10.1093/imrn/rnac370
State	Published - 1 Nov 2023

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1093/imrn/rnac370

Cite this

@article{2b67efe49da341af8b86e35df0cd73c3,

title = "The Minimal Ramification Problem for Rational Function Fields over Finite Fields",

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.",

author = "Lior Bary-Soroker and Alexei Entin and Arno Fehm",

year = "2023",

month = nov,

day = "1",

doi = "https://doi.org/10.1093/imrn/rnac370",

language = "الإنجليزيّة",

volume = "2023",

pages = "18199--18253",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "21",

}

TY - JOUR

T1 - The Minimal Ramification Problem for Rational Function Fields over Finite Fields

AU - Bary-Soroker, Lior

AU - Entin, Alexei

AU - Fehm, Arno

PY - 2023/11/1

Y1 - 2023/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85178060311&partnerID=8YFLogxK

U2 - https://doi.org/10.1093/imrn/rnac370

DO - https://doi.org/10.1093/imrn/rnac370

M3 - مقالة

SN - 1073-7928

VL - 2023

SP - 18199

EP - 18253

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 21

ER -

The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this