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Triple linkage of quadratic Pfister forms

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 \({\text {char}}(F) \ne ~2\) and \(u(F)=4\), then every three quaternion algebras share a common maximal subfield.

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Acknowledgements

We thank the referee for useful suggestions that improved the clarity of the paper. The second author was supported by Automorphism groups of locally finite trees (G011012) with the Research Foundation, Flanders, Belgium (F.W.O. Vlaanderen).

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Correspondence to Andrew Dolphin.

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Chapman, A., Dolphin, A. & Leep, D.B. Triple linkage of quadratic Pfister forms. manuscripta math. 157, 435–443 (2018). https://doi.org/10.1007/s00229-017-0996-6

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Mathematics Subject Classification

  • 11E81 (Primary)
  • 11E04
  • 16K20
  • 11R52 (Secondary)