Logarithmic prismatic cohomology II

TL;DR

This paper advances the theory of logarithmic prismatic cohomology by establishing de Rham and étale comparison theorems, constructing a Nygaard filtration, and relating F-crystals to Z_p-local systems in the logarithmic context.

Contribution

It completes the proof of key comparison theorems for logarithmic prismatic cohomology, generalizing previous results and introducing new structures like the Nygaard filtration.

Findings

Proved de Rham and étale comparison theorems for logarithmic prismatic cohomology.

Constructed a suitable Nygaard filtration in the logarithmic setting.

Established a relation between F-crystals and Z_p-local systems in the logarithmic context.

Abstract

We continue to study the logarithmic prismatic cohomology defined by the first author, and complete the proof of the de Rham comparison and \'etale comparison generalizing those of Bhatt and Scholze. We prove these comparisons for a derived version of logarithmic prismatic cohomology, and, along the way, we construct a suitable Nygaard filtration and explain a relation between $F$-crystals and $\mathbb{Z}_p$-local systems in the logarithmic setting.