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arXiv · 1609.01403

On triviality of reduced Whitehead group over Henselian fields

A. Soman
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Abstract

Let $F$ be a Henselian field of $q$-cohomological dimension $3$, where $q$ is a prime. Let $\Gamma_F$ be the totally ordered abelian value group of $F$ and let $D$ be a central division algebra over $F$ of index a power of $q$ such that the characteristic of the residue field, $\overline{F}$ is coprime to $q$. We show that when $1\leq\dim_{\mathbb{F}_q}(\Gamma_F/q\Gamma_F)\leq 3$, the reduced Whitehead group of $D$ is trivial.

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A. Soman. 2016-09-06. On triviality of reduced Whitehead group over Henselian fields. https://arxiv.org/abs/1609.01403

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