6 problems

Let $X$ be a smooth $p$-adic analytic Artin stack, and let $L(X)$ denote its associated light condensed anima. Clausen's conjecture. Étale-locally, $L(X)$ is a light profinite anim…

Light profiniteness conjecture. Étale locally, the associated light condensed anima is a light profinite anima.

Condensed and bornological geometry model conjecture. The models of geometry in condensed mathematics, such as analytic stacks, and the models of geometry based on bornological rin…

Let $n\geq 2$, let $X$ be a finite extension of a local nonarchimedean field, let $G(X)$ be a reductive group, and let $\mathrm{Gal}_{X,n}$ and $\mathrm{Weil}_{X,n}$ denote the cor…

Let $X$ be a finite extension of a local nonarchimedean field, let $G(X)$ be a $z$-adic reductive group, and let $\mathrm{Gal}_{X,2}$ denote the two-fold covering of the Galois gro…

The condensed Whitehead conjecture. Suppose that $A$ is an abelian group, $\mathbb{B}$ is a complete Boolean algebra, and