  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.
