Annihilators of differential forms over over fields of characteristic p

TL;DR

This paper investigates the structure of annihilators of differential forms over fields of characteristic p, providing specific descriptions and exploring their relation to kernels of restriction maps in purely inseparable extensions.

Contribution

It offers new descriptions of annihilators of differential forms and establishes a connection with kernels of restriction maps in purely inseparable field extensions.

Findings

Descriptions of annihilators for special cases

Connection between annihilators and kernels of restriction maps

Insights into differential forms over fields of characteristic p

Abstract

Let $F$ be a field of characteristic $p$ and let $\Omega^n(F)$ 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 $\Omega^n(F) \to \Omega^n(E)$ for purely inseparable field extensions $E/F$.