On the m-torsion Subgroup of the Brauer Group of a Global Field

Wen-Chen Chi, Hung-Min Liao, Ki-Seng Tan

Published 2007-01-02Version 1

In this note, we give a short proof of the existence of certain abelian extension over a given global field $K$. This result implies that for every positive integer $m$, there exists an abelian extension $L/K$ of exponent $m$ such that the $m$-torsion subgroup of $\Br(K)$ equals $\Br(L/K)$.