Comparison of prismatic cohomology and derived de Rham cohomology

2020/12/28 by Shizhang Li, Tong Liu, Li, Shizhang +1 · 2 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11F80 #14F30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.14064

openalex publication_date 2020/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a comparison isomorphism between prismatic cohomology and derived de Rham cohomology respecting various structures, such as their Frobenius actions and filtrations. As an application, when X is a proper smooth formal scheme over \mathcal O_K with K being a p-adic field, we improve Breuil--Caruso's theory on comparison between torsion crystalline cohomology and torsion étale cohomology.

Cited by

• A prismatic approach to (φ, G)-modules and F-crystals
• Bounding crystalline torsion from étale torsion

Related

• Crystalline cohomology and de Rham cohomology
• An integral comparison of crystalline and de Rham cohomology
• On the cohomology of p-adic analytic spaces, I: The basic comparison theorem
• p-adic derived de Rham cohomology
• Overconvergent prismatic cohomology