| Résume | Following a conjecture of Le Bras, I will explain the construction of a cohomology theory for rigid-analytic varieties over C_p (without properness nor smoothness assumptions), taking values in the category of filtered quasi-coherent complexes over the Fargues-Fontaine curve, which interpolates between other known rational p-adic cohomology theories for rigid-analytic varieties: namely, the rational p-adic pro-étale cohomology, the Hyodo-Kato cohomology defined by Colmez-Niziol, and the infinitesimal cohomology over the positive de Rham period ring. If time permits, I will also report on an expected integral variant of such cohomology theory. |
