Abelian extensions of global fields with constant local degrees

2004/12/08 by Hershy Kisilevsky, Kisilevsky, Hershy, Jack Sonn +1
Mathematics · #11R20 #11R37 #12F10 #16K50 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Biology Tumor Growth #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11R20 #msc:11R37 #msc:12F10 #msc:16K50

paper · pdf · doi:10.48550/arxiv.math/0412176

7 pages. The present version gives a different proof of the main result. In the previous version, a special case was overlooked, which the previous proof did not cover

openalex publication_date 2004/12/08 · arxiv created 2005/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a global field K and a positive integer n, there exists an abelian extension L/K (of exponent n) such that the local degree of L/K is equal to n at every finite prime of K, and is equal to two at the real primes if n=2. As a consequence, the n-torsion subgroup of the Brauer group of K is equal to the relative Brauer group of L/K.

Related

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