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arXiv · 1706.04929

Triple Linkage of Quadratic Pfister Forms

Adam Chapman·Andrew Dolphin·David B. Leep
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Abstract

Given a field $F$ of characteristic 2, we prove that if every three quadratic $n$-fold Pfister forms have a common quadratic $(n-1)$-fold Pfister factor then $I_q^{n+1} F=0$. As a result, we obtain that if every three quaternion algebras over $F$ share a common maximal subfield then $u(F)$ is either $0,2$ or $4$. We also prove that if $F$ is a nonreal field with $\operatorname{char}(F) \neq 2$ and $u(F)=4$, then every three quaternion algebras share a common maximal subfield.

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Adam Chapman, Andrew Dolphin, David B. Leep. 2017-06-15. Triple Linkage of Quadratic Pfister Forms. https://arxiv.org/abs/1706.04929

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