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may 2020 Field of Iterated Laurent Series and its Brauer Group
Adam Chapman
Bull. Belg. Math. Soc. Simon Stevin 27(1): 1-6 (may 2020). DOI: 10.36045/bbms/1590199296

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. "Field of Iterated Laurent Series and its Brauer Group." Bull. Belg. Math. Soc. Simon Stevin 27 (1) 1 - 6, may 2020. https://doi.org/10.36045/bbms/1590199296

Information

Published: may 2020
First available in Project Euclid: 23 May 2020

zbMATH: 07213652
MathSciNet: MR4102695
Digital Object Identifier: 10.36045/bbms/1590199296

Subjects:
Primary: 11E04, 11E81, 16K20, 16W60

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 1 • may 2020
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