Annihilators of differential forms over fields of characteristic p

Abstract

Let F be a field of characteristic p and let Ωn(F) be the F-vector space of n-differential forms. In this work, we will study the annihilator of differential forms, give specific descriptions for special cases and show a connection between these annihilators and the kernels of the restriction map Ωn(F)→Ωn(E) for purely inseparable field extensions E/F.