11 problems

Let $K$ be a finite extension of $\mathbb{Q}_p$. Write $\mathcal{D}(\ast/GL_n(K)^{\la})$ for the stable $\infty$-category of locally analytic representations of $GL_n(K)$, let…

Assume that $E$ is a finite extension of $\mathbb Q_p$, and let $F$ be the function field of the schematic Fargues–Fontaine curve $X_C^{\mathrm{sch}}$ in the notation of the source…

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…

Let $A^h$ be a local chart arising from the Bambozzi–Kremnizer spectrum of a Banach algebra over $\mathbb{Q}_p$ or $\mathbb{F}_p((t))$, and let $S$ be the coefficient ring. For int…

Fargues–Fontaine cohomology conjecture. There exists a motivic realization functor on compact rigid motives

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 i…

Let $X$ be the Fargues–Fontaine curve, and let $\mathcal{E}$ be a vector bundle on $X$. For each rational slope $mu$, write $\mathcal{E}^{geq mu}$ for the subbundle determined by t…

Let $X$ be the Fargues–Fontaine curve, and let $\mathcal{C}$ be the division algebra introduced by Colmez. The Brauer–Severi variety of a central division algebra is the variety pa…

Let $C$ be an algebraically closed $p$-adic field, let $\operatorname{FF}_C$ be the Fargues–Fontaine curve with distinguished point $\infty$, and let $X$ be a quasicompact separate…

Let $G$ be a reductive group, let $\mathrm{Bun}_G$ be the stack of $G$-bundles on the Fargues–Fontaine curve, and let a local $L$-parameter be given. Fargues's geometric Langlands…

Fargues's conjecture. The Banach algebra $B_I$ is strongly noetherian: for every $n\geq 1$, the Tate algebra