6 problems

For $0<r_2<r_1<1$, let … be the Banach ring constructed as the non-expanding colimit of the rings $\mathbb{Z}\{(x/r)^{1/n}\}$ under the morphisms $\alpha_{n,m}$. Nuclearity conject…

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…

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 $E$ 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 $C$ 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…

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