Mathematical Research Letters

Volume 13, Issue 4, July 2006 pp. 599-605.

Abelian extensions of global fields with constant local degree

Authors: Hershy Kisilevsky (1), and Jack Sonn (2)
Author institution: Concordia University (1), and Technion--Israel Institute of Technology (2)

Summary: 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 $L/K$.

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