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arXiv · 1905.07068

Field of Iterated Laurent Series and its Brauer Group

Adam Chapman
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Abstract

The symbol length of ${_pBr}(k(\!(\alpha_1)\!)\dots(\!(\alpha_n)\!))$ for an algebraically closed field $k$ of $\operatorname{char}(k) \neq p$ is known to be $\lfloor \frac{n}{2} \rfloor$. We prove that the symbol length for the case of $\operatorname{char}(k) = p$ is rather $n-1$. We also show that pairs of anisotropic quadratic or bilinear $n$-fold Pfister forms over this field need not share an $(n-1)$-fold factor.

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Adam Chapman. 2019-05-16. Field of Iterated Laurent Series and its Brauer Group. https://arxiv.org/abs/1905.07068

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