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We associate an Albert form to any pair of cyclic algebras of prime degree$p$ over a field $F$ with $\operatorname{char}(F)=p$ which coincides with theclassical Albert form when $p=2$. We prove that if every Albert form isisotropic then $H^4(F)=0$. As a result, we obtain that if $F$ is a linked fieldwith $\operatorname{char}(F)=2$ then its $u$-invariant is either $0,2,4$ or$8$.

Differential Forms, Linked Fields and the $u$-Invariant