nLab
prismatic cohomology

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Algebraic topology

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

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Idea

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

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

References

For some introductory comments see

Last revised on January 9, 2020 at 03:58:39. See the history of this page for a list of all contributions to it.