A theory of Galois descent for finite inseparable extensions

TL;DR

This paper generalizes Galois descent to finite inseparable extensions using the Heerma-Galois group, expanding the theoretical framework for understanding such field extensions.

Contribution

It introduces a new approach to Galois descent for inseparable extensions via the Heerma-Galois group, broadening the scope of classical Galois theory.

Findings

Generalization of Galois descent to inseparable extensions

Use of Heerma-Galois group for automorphisms

Framework applicable to finite modular normal extensions

Abstract

We present a generalization of Galois descent to finite modular normal field extension $L/K$, using the Heerma-Galois group $Aut(L[\bar{X}]/K[\bar{X}])$ where $L[\bar{X}]=L[X]/(X^{p^e})$ and $e$ is the exponent of $L$ over $K$.