Norm tori of etale algebras and unramified Brauer groups

2021/10/12 by Eva Bayer‐Fluckiger, Bayer-Fluckiger, Eva, Ting-Yu Lee +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.05993

openalex publication_date 2021/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a field, and let L be an étale k-algebra of finite rank. If a is a nonzero element in k, let X_a be the affine variety defined by the norm equation N_L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial description of the unramified Brauer group of X_a.

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