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# Mathematical Research Letters

## Volume 13 (2006)

### Number 4

### Abelian extensions of global fields with constant local degree

Pages: 599 – 605

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n4.a9

#### Authors

#### Abstract

We prove that, 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, we prove that the $n$-torsion subgroup of the Brauer group of $K$ is equal to the relative Brauer group of $L/K$.