nLab
prismatic cohomology
Context
Cohomology
cohomology

Special and general types
Special notions
Variants
Operations
Theorems
Algebraic topology
$(\infty,1)$ -Topos Theory
(∞,1)-topos theory

Background
Definitions
elementary (∞,1)-topos

(∞,1)-site

reflective sub-(∞,1)-category

(∞,1)-category of (∞,1)-sheaves

(∞,1)-topos

(n,1)-topos , n-topos

(∞,1)-quasitopos

(∞,2)-topos

(∞,n)-topos

Characterization
Morphisms
Extra stuff, structure and property
hypercomplete (∞,1)-topos

over-(∞,1)-topos

n-localic (∞,1)-topos

locally n-connected (n,1)-topos

structured (∞,1)-topos

locally ∞-connected (∞,1)-topos , ∞-connected (∞,1)-topos

local (∞,1)-topos

cohesive (∞,1)-topos

Models
Constructions
structures in a cohesive (∞,1)-topos

Contents
Idea
A type of cohomology attached to prisms, which are $\delta$ -rings equipped with an ideal satisfying some conditions. (The pair $(A, I)$ is a prism when $I$ is an ideal of a $\delta$ -ring $A$ defining a Cartier divisor on its spectrum $Spec(A)$ such that $A$ is derived $(p,I)$ -complete, and $p \in I + \phi(I)A$ .)

Roughly, it is a unified construction of various $p$ -adic cohomology theories, including étale cohomology , de Rham cohomology and crystalline cohomology , as well as the so far conjectural $q$ -de Rham cohomology of Peter Scholze .

References
For some introductory comments see