Fargues–Scholze categorical Langlands conjecture

Let $K'$ be a finite extension of $\mathbb{Q}_p$, let $G$ be the corresponding reductive group, let $A$ be a coefficient ring, and let $\mathrm{Bundle}_{G}(\mathrm{FF}_{\square})$ and $\mathrm{Stack}_{L,{G}^\mathrm{dual},A}/{G}^\mathrm{dual}$ denote respectively the stack of $G$-bundles on the relevant Fargues–Fontaine curve and the stack of $L$-parameters. Consider the derived $\infty$-categories

$$\mathrm{DerivedCat}(\mathrm{Bundle}_{G}(\mathrm{FF}_{\square}))_{\mathrm{Coeff}: A}$$

and

$$\mathrm{DerivedCat}_{\mathrm{bounded},\mathrm{coherent},\mathrm{Nilpotent}}(\mathrm{Stack}_{L,{G}^\mathrm{dual},A}/{G}^\mathrm{dual}).$$

Fargues–Scholze's categorical Langlands conjecture. There is a canonical isomorphism between these two $\infty$-categories.

This is the categorical form of the Fargues–Scholze geometrization of the Langlands program, relating complexes on the stack of $G$-bundles to bounded coherent nilpotent sheaves on the stack of $L$-parameters. The source presents this as the usual, non-mixed-parity conjecture; its status is not established in the supplied text.