Logarithmic Combinatorial Differentials

TL;DR

This paper develops a geometric framework for understanding higher-order differentials and the de Rham complex in the context of morphisms of fine log schemes, enhancing the theoretical tools available in logarithmic geometry.

Contribution

It introduces a geometric description of higher-order differential sheaves and defines the de Rham complex within the setting of fine log schemes, providing new insights into their structure.

Findings

Provides a geometric interpretation of $ abla^n_{X/S}$ sheaves

Defines the de Rham complex for fine log schemes

Enhances understanding of differentials in logarithmic geometry

Abstract

Given a morphism $X \to S$ of fine log schemes, we develop a geometric description of the sheaves of higher-order differentials $\Omega^n_{X/S}$ for $n > 1$, as well as a definition of the de Rham complex in terms of this description.