Appears in collection : 2023 IHES Summer School – Recent Advances in Algebraic K-theory

Prismatic cohomology originally arose from the study of topological cyclic homology and comes in two flavors: Absolute prismatic cohomology, which is more tightly connected to topological cyclic homology, and the comparatively more computable relative prismatic cohomology, where one works relative to a fixed base prism. In this talk, I want to explain "prismatic cohomology relative delta-rings", a mutual generalization interpolating between the two.