The Fargues-Fontaine de Rham stack

The analytic de Rham stack is a new construction in Analytic Geometry whose theory of quasi-coherent sheaves encodes a notion of p-adic D-modules. It has the virtue that can be defined even under lack of differentials (eg. for perfectoid spaces or Fargues-Fontaine curves). In this talk I will mention some applications of the theory of the analytic de Rham stack in p-adic Hodge theory in the form of the Fargues-Fontaine de Rham stacks; analytic objects whose cohomology theories refine the usual de Rham cohomology of rigid spaces in the form of the Fargues-Fontaine de Rham cohomology of Le Bras-Vezzani.