The Tamely Ramified Geometric Quantitative Minimal Ramification Problem

2022/11/30 by Mark Shusterman, Shusterman, Mark · 2 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2211.16983

openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a large finite field version of the Boston--Markin conjecture on counting Galois extensions of the rational function field with a given Galois group and the smallest possible number of ramified primes. Our proof involves a study of structure groups of (direct products of) racks.

Cited by

• Representation stability for ordered Hurwitz spaces
• Burnside rings for racks and quandles

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