11 problems

Let $X$ be a perfectoid boundary carrier equipped with a condensed sheaf/module $\mathcal{F}$ of sources and operators, and let $X^{\flat}$ be its tilt. Assume the holographic gene…

Global perfectoidness conjecture. This inverse limit is representable by a perfectoid space. Perfectoidness at infinite $p$-level is a central representability question for Shimura…

Let $X/C$ be a smooth proper connected variety of pure dimension $d$ with globally generated $1$-forms, and fix a point $x\in X(C)$. Let … be a closed subgroup. The canonical map s…

Let $n$ be a positive integer and, for each integer $d$ with $0<d<n$, let $W_{n,d}$ be the space defined in the paper from the corresponding local geometric construction. Perfectoi…

Geometric Sen perfectoidness conjecture. The morphism $\theta_{\widetilde{X}}$ is surjective if and only if $\widetilde{X}$ is a perfectoid space.

Let $I=\{1,2\}$, let $M$ be a $\Phi$-equivariant $F$-isocrystal $(M,\varphi,\varphi_1,\varphi_2)$ in the category…

Kummer pro-étale extension conjecture. The construction developed in the section should extend to suitable Kummer pro-étale sites with logarithmic perfectoid subdomains forming a b…

Let $E$ be the local field in the paper, let $\operatorname{Gr}$ be the corresponding affine Grassmannian, and let … be the Beauville–Laszlo morphism. Beauville–Laszlo uniformizati…

Let $K$ be a perfectoid field, let $(A,A^+)$ be a complete affinoid $K$-algebra for which $A^+$ has the $p$-adic topology, and set $X=\operatorname{Spa}(A,A^+)$. Assume that $X$ ha…

Let $K$ be a perfectoid field, let $(A,A^+)$ be a complete affinoid $K$-algebra, and set $X=\operatorname{Spa}(A,A^+)$. Assume that $X$ has a cover by rational subsets…

Let $K$ be a perfectoid field with tilt $K^\flat$, let $X\subset \mathbb{P}^n_K$ be a smooth closed subscheme, and let $\tilde{X}\subset (\mathbb{P}^n_K)^\mathrm{ad}$ be a small op…