Title: 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 $\operatorname{char}(F)=p$ 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 $\operatorname{char}(F)=2$ then its $u$-invariant is either $0,2,4$ or
$8$.