Abelian extensions of global fields with constant local degrees
Number Theory
2007-05-23 v4 Rings and Algebras
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.
Cite
@article{arxiv.math/0412176,
title = {Abelian extensions of global fields with constant local degrees},
author = {Hershy Kisilevsky and Jack Sonn},
journal= {arXiv preprint arXiv:math/0412176},
year = {2007}
}
Comments
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