The behaviour of differential and quadratic forms under purely inseparable field extensions

In this paper, we will find the generators of the Witt-kernel of quadratic forms in characteristic two for purely inseparable field extension $E/F$. This will be done using Kato's isomorphism $I^n(F)W_q(F)/I^{n+1}W_q(F) \to H_2^{n+1}(F)$ together with some theory of quadratic forms.