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Let $F$ be a field of characteristic $p>0$ and let $\Omega^n(F)$ be the$F$-vector space of $n$-differential forms over $F$. In this work we will studythe behaviour of $\Omega^n(F)$ under iterated function field extensions of$p$-forms. We will use results from a previous work to rewrite the kernel ofthe restriction map $\Omega^n(F) \to \Omega^n(F(\varphi_1,\ldots,\varphi_r))$to a set of differential forms annihilated by specific forms given by the normfields of $\varphi_1,\ldots,\varphi_r$. We will close this work by translatingthe new resluts to the theory of bilinear forms over fields of characteristic$2$.

Function field extensions and annihilators of differential forms in characteristic p and bilinear forms in characteristic 2