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arXiv · 2207.02154

On algebraic central division algebras over Henselian fields of finite absolute Brauer $p$-dimensions and residually arithmetic type

Ivan D. Chipchakov
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Abstract

Let $(K, v)$ be a Henselian field with a residue field $\widehat K$ and value group $v(K)$, and let $\mathbb{P}$ be the set of prime numbers. This paper finds conditions on $K$, $v(K)$ and $\widehat K$ under which every algebraic associative central division $K$-algebra $R$ contains a central $K$-subalgebra $\widetilde R$ decomposable into a tensor product of central $K$-subalgebras $R _{p}$, $p \in \mathbb{P}$, of finite $p$-primary dimensions $[R _{p}\colon K]$, such that each finite-dimensional $K$-subalgebra $\Delta $ of $R$ is isomorphic to a $K$-subalgebra $\widetilde \Delta $ of $\widetilde R$.

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Ivan D. Chipchakov. 2022-07-05. On algebraic central division algebras over Henselian fields of finite absolute Brauer $p$-dimensions and residually arithmetic type. https://arxiv.org/abs/2207.02154

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