Special Year Seminar

Motivated by the desire to express in terms of de Rham data the pro-étale cohomology with non-trivial $\mathbb{Q}_p$-coefficients of rigid spaces $X$, defined over $\mathbb{Q}_p$ or $\mathbb{C}_p$, I will explain how to define D-modules on the relative Fargues-Fontaine curve attached to $X$, and why it is interesting to consider such objects. Then, I will outline how the cohomology of such D-modules generalizes to coefficients the Hyodo-Kato cohomology for rigid spaces defined by Colmez-Nizioł.

This is based on joint work in progress with Johannes Anschütz, Arthur-César Le Bras, and Juan Esteban Rodriguez Camargo.