On log differentials of local fields

TL;DR

This paper establishes a logarithmic analogue of Fontaine's fundamental theorem concerning the differentials of the algebraic closure of a local field over the base field, extending classical results into the logarithmic setting.

Contribution

It introduces a logarithmic version of Fontaine's theorem, providing new insights into the structure of differentials in local field extensions.

Findings

Proves a logarithmic analogue of Fontaine's theorem.

Extends classical differential results to the logarithmic context.

Enhances understanding of local field extensions in logarithmic geometry.

Abstract

We prove a logarithmic version of Fontaine's classic result on differentials of $\mathcal{O}_{\bar K}$ over $\mathcal{O}_K$.