Sur la cohomologie étale de la courbe de Fargues-Fontaine

In this article the étale cohomology of constructible torsion sheaves on the étale site of the algebraic resp. adic Fargues-Fontaine curve is analyzed. In the $\mathrm{\ell }\mathrm{\ne }p$-torsion case, two conjectures of Fargues are verified: vanishing in degrees greater than two and the comparison between the étale cohomology of the adic and the algebraic curve. In the $p$-torsion case, under a certain assumption, the vanishing of the étale cohomology in degrees greater than two of those Zariski-constructible sheaves on the adic curve that come via pullback from the algebraic curve is proven.