The Minimal Ramification Problem for Rational Function Fields over Finite Fields

Lior Bary-Soroker; Alexei Entin; Arno Fehm

doi: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

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10.1093/imrn/rnac370

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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.",

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AU - Fehm, Arno

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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.

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U2 - 10.1093/imrn/rnac370

DO - 10.1093/imrn/rnac370

M3 - مقالة

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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

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