Prismatic cohomology of rigid analytic spaces over de Rham period ring

TL;DR

This paper extends prismatic cohomology to rigid analytic spaces with singularities, using Fontaine's de Rham period ring, inspired by Bhatt-Scholze's foundational work.

Contribution

It introduces a new framework for prismatic cohomology applicable to singular rigid analytic spaces with coefficients over de Rham period ring.

Findings

Defines prismatic cohomology for singular spaces

Establishes foundational properties of the cohomology theory

Connects to Fontaine's de Rham period ring

Abstract

Inspired by Bhatt-Scholze, we introduce prismatic cohomology for rigid analytic spaces with l.c.i singularities, with coefficients over Fontaine's de Rham period ring.