On the m-torsion Subgroup of the Brauer Group of a Global Field

2007/01/02 by Wen-Chen Chi, Chi, Wen-Chen, Hung-Min Liao +3
Mathematics · #11K60 #11R29 #11R34 #11R37 #11R56 #11R58 #11S15 #11S25 #11S37 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT #msc:11K60 #msc:11R29 #msc:11R34 #msc:11R37 #msc:11R56 #msc:11R58 #msc:11S15 #msc:11S25 #msc:11S37

paper · pdf · doi:10.48550/arxiv.math/0701052

5 pages

arxiv created 2007/01/02 · openalex publication_date 2007/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we give a short proof of the existence of certain abelian extension over a given global field K. This result implies that for every positive integer m, there exists an abelian extension L/K of exponent m such that the m-torsion subgroup of \Br(K) equals \Br(L/K).

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