Logarithmic de Rham--Witt complexes via the D\'ecalage operator

TL;DR

This paper introduces a new formalism for logarithmic de Rham--Witt complexes, generalizing previous results and providing a more direct proof of the log crystalline comparison in semistable cases.

Contribution

It develops a novel formalism for log de Rham--Witt complexes that extends prior work and simplifies the proof of log crystalline comparison for semistable schemes.

Findings

Generalizes de Rham--Witt complexes to the logarithmic setting

Aligns with existing theories for log-smooth schemes of log-Cartier type

Provides a more direct proof of log crystalline comparison in semistable reduction

Abstract

We provide a new formalism of de Rham--Witt complexes in the logarithmic setting. This construction generalizes a result of Bhatt--Lurie--Mathew, and agrees with those of Hyodo--Kato and Matsuue for log-smooth schemes of log-Cartier type. We then apply our formalism to obtain a more direct proof of the log crystalline comparison of A_inf-cohomology in the case of semistable reduction, which is established by Cesnavicius--Koshiwara.