# nLab prismatic cohomology

cohomology

### Theorems

#### $(\infty,1)$-Topos Theory

(∞,1)-topos theory

## 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.