Abelian extensions of global fields with constant local degrees
Abstract
Description
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.
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
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