Fargues's cohomological dimension conjecture for constructible sheaves on the Fargues–Fontaine curve

Let $E$ be a $p$-adic field, let $F$ be the coefficient field defining the Fargues–Fontaine curve, and let $X^{\operatorname{alg}}_{E,F}$ denote its algebraic version. Let $\mathcal{F}$ be a constructible $\mathbb{Z}/n\mathbb{Z}$-module on the étale site of $X^{\operatorname{alg}}_{E,F}$. Fargues's vanishing conjecture. For every $i\geq 3$, one has

$$H^{i}(X^{\operatorname{alg}}_{E,F},\,\mathcal{F})=0.$$

This predicts that constructible torsion sheaves on the algebraic Fargues–Fontaine curve have no étale cohomology above degree $2$. The context records the analogous vanishing as unknown even for local systems, so the conjecture remains open.