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arXiv · 1903.09063

Noncyclic Division Algebras over Fields of Brauer Dimension One

Eric Brussel
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Abstract

Let $K$ be a complete discretely valued field of rank one, with residue field $\Q_p$. It is well known that period equals index in $\Br(K)$. We prove that when $p=2$ there exist noncyclic $K$-division algebras of every $2$-power degree divisible by four. Otherwise, every $K$-division algebra is cyclic.

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Eric Brussel. 2019-03-21. Noncyclic Division Algebras over Fields of Brauer Dimension One. https://arxiv.org/abs/1903.09063

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