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Differential forms, linked fields, and the u-invariant

Abstract

We associate an Albert form to any pair of cyclic algebras of prime degree p over a field F with 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 char(F) = 2, then its u-invariant is either 0, 2, 4, or 8

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