Fargues's étale cohomology comparison conjecture for the Fargues–Fontaine curve

Let $E$ be a $p$-adic field, let $F$ be the coefficient field defining the Fargues–Fontaine curve, and let $X^{\operatorname{alg}}_{E,F}$ and $X^{\operatorname{ad}}_{E,F}$ denote its algebraic and adic versions. Let $u\colon (X^{\operatorname{ad}}_{E,F})_{\operatorname{ét}}\to (X^{\operatorname{alg}}_{E,F})_{\operatorname{ét}}$ be the morphism of étale sites, and for a constructible $\mathbb{Z}/n\mathbb{Z}$-module $\mathcal{F}$ on $(X^{\operatorname{alg}}_{E,F})_{\operatorname{ét}}$, write $\mathcal{F}^{\operatorname{ad}}=u^*(\mathcal{F})$. Fargues's comparison conjecture. For every $i\geq 0$, there is an isomorphism

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

This conjecture predicts that algebraic and adic étale cohomology agree for arbitrary constructible torsion coefficients. The comparison is motivated by the known relationship between the étale cohomology of local systems on the curve and Galois cohomology, while its validity in all degrees for constructible sheaves remains open.