  In this article the \'etale cohomology of constructible torsion sheaves on
the \'etale site of the algebraic resp. adic Fargues-Fontaine curve is
analyzed. In the $\ell\neq p$-torsion case, two conjectures of Fargues are
verified: vanishing in degrees greater than two and the comparison between the
\'etale cohomology of the adic and the algebraic curve. In the $p$-torsion
case, under a certain assumption, the vanishing of the \'etale 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.
