2016/06/15 by Ming-chang Kang, Kang, Ming-chang
Mathematics · #12F10 #13A50 #14E08 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1606.04611
openalex publication_date 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p be a prime number and ζp be a primitive p-th root of unity in \bmC. Let k be a field and k(x0,…,xp-1) be the rational function field of p variables over k. Suppose that G=⟨σ⟩ ≃ Cp acts on k(x0,…,xp-1) by k-automorphisms defined as σ:x0↦ x1↦⋯↦ xp-1↦ x0. Denote by P the set of all prime numbers and define P0=\p∈ P:\bmQ(ζp) is of class number one\. Theorem. If k is an algebraic number field and p∈ P\backslash (P0∪ Pk), then k(x0,…,xp-1)G is not stably rational over k where Pk=\p∈ P: p is ramified in k\.