Abstract
We associate an Albert form to any pair of cyclic algebras of prime degree p over a field F with \({\text {char}}(F)=p\) which coincides with the classical Albert form when \(p=2\). We prove that if every Albert form is isotropic, then \(H^4(F)=0\). As a result, we obtain that if F is a linked field with \({\text {char}}(F)=2\), then its u-invariant is either 0, 2, 4, or 8.
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Chapman, A., Dolphin, A. Differential forms, linked fields, and the u-invariant. Arch. Math. 109, 133–142 (2017). https://doi.org/10.1007/s00013-017-1059-7
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DOI: https://doi.org/10.1007/s00013-017-1059-7