Espaces de Banach-Colmez et faisceaux cohérents sur la courbe de Fargues-Fontaine

Abstract

We give a new definition, simpler but equivalent, of the abelian category of Banach-Colmez spaces introduced by Colmez, and we explain the precise relationship with the category of coherent sheaves on the Fargues-Fontaine curve. One goes from one category to the other by changing the t-structure on the derived category. Along the way, we obtain a description of the pro-étale cohomology of the open disk and the affine space, of independent interest.

In French, comments welcome !

References in corpus (3)

• Geometrization of the local Langlands correspondence: an overview
• Overconvergent relative de Rham cohomology over the Fargues-Fontaine curve
• Geometric syntomic cohomology and vector bundles on the Fargues-Fontaine curve

Cited by in corpus (4)

• Extensions of Vector Bundles on the Fargues-Fontaine Curve
• Universal norms and the Fargues-Fontaine curve
• On the $p$-adic pro-étale cohomology of Drinfeld symmetric spaces
• Almost $C_p$ Galois representations and vector bundles