# 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-03018432
Contributor : Arthur-César Le Bras Connect in order to contact the contributor
Submitted on : Friday, November 26, 2021 - 11:54:38 AM
Last modification on : Thursday, December 2, 2021 - 3:49:35 AM

### File

1801.00429.pdf
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### Identifiers

• HAL Id : hal-03018432, version 1
• ARXIV : 1801.00429

### Citation

Arthur-César Le Bras. Overconvergent relative de Rham cohomology over the Fargues-Fontaine curve. 2021. ⟨hal-03018432⟩

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