Comparison of prismatic cohomology and derived de Rham cohomology

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.

3rd version. Fix some typos (keep filtration comparison only for transversal prism as version 1)

References in corpus (1)

• Integral p-adic Hodge theory of formal schemes in low ramification

Cited by in corpus (3)

• Topologization and Functional Analytification I: Intrinsic Morphisms of Commutative Algebras
• Crystalline condition for $A_{\inf }$-cohomology and ramification bounds
• A prismatic approach to $(\phi ,\hat{G})$-modules and $F$-crystals