Overconvergent relative de Rham cohomology over the Fargues-Fontaine curve

Abstract

We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over ${\mathbf{C}}_p$ (or more general base fields), taking values in the category of vector bundles on the Fargues-Fontaine curve, which extends (in a suitable sense) Hyodo-Kato cohomology when the rigid space has a semi-stable proper formal model over the ring of integers of a finite extension of ${\mathbf{Q}}_p$. This cohomology theory factors through the category of rigid analytic motives of Ayoub.

New version ; modified Introduction and Section 6

References in corpus (1)

• Cohomologie p-adique de la tour de Drinfeld: le cas de la dimension 1

Cited by in corpus (4)

• Espaces de Banach-Colmez et faisceaux cohérents sur la courbe de Fargues-Fontaine
• Spreading out the Hodge filtration in non-archimedean geometry
• On the $p$-adic pro-étale cohomology of Drinfeld symmetric spaces
• The de Rham-Fargues-Fontaine cohomology