59 problems

Let $L/\mathbb{Q}_p$ be a $p$-adic field and let $X/L$ be a smooth rigid analytic variety. Let $\mathrm{AdmPair}^{\mathrm{basic},\mathrm{pgr}}(X^\diamond)$ denote basic admissible…

Let $Y$ be a smooth partially proper rigid analytic variety over $K$ of dimension $d$, let $\partial Y$ denote its boundary, and let…

Let $X$ be a proper rigid analytic space over $K$. A formal versal deformation of $X$ is the formal deformation supplied by the local deformation theory of $X$. Global versal-famil…

Schneider–Stuhler's conjecture. The filtration $F^\bullet$ essentially coincides with the monodromy filtration $M_\bullet$.

Let $X$ be a connected smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. Let $\mathrm{R}p\mathrm{MT}^w$ d…

Let $X$ be a connected smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. Relative p-adic monodromy conjec…

Let $X$ be a smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. A point $x\in X$ has rank $1$ if it is a r…

The relativistic $p$-adic sunscreen conjecture. The set

Let $L$ be a strict $p$-adic field, let $C=\overline{L}^{\wedge}$, let $X/L$ be a smooth rigid analytic variety, and let $\tilde{X}/X$ be a potentially unramified object of…

Potentially unramified tower conjecture. The following assertions hold: (1) $\hat{\tilde{X}}$ is an adic space and $(\hat{\tilde{X}})^\diamond=\tilde{X}^\diamond$; (2) the natural…

Let $K$ be a finite extension of ${\bf Q}_p$, and let $Y$ be a smooth partially proper rigid analytic variety over $K$ of dimension $d$. Write…

Let $K$ be a finite extension of ${\bf Q}_p$, let $Y$ be a smooth partially proper rigid analytic variety over $K$, and let $r\geq 0$. Let…

Let $Y$ be a smooth partially proper rigid analytic variety over $K$, and suppose that its Hyodo–Kato cohomology groups are of finite rank over $C^{\operatorname{nr}}$. These group…

Let $R$ be a topologically finitely generated and $p$-complete ${\mathcal{O}}_{\mathbf{C}}$-algebra, and let … be an ${\mathcal{O}}_{\mathbf C}$-homomorphism. A rational Hodge--Tat…

Let $\mathfrak{X}$ be the smooth formal curve under consideration, and let $\mathcal{D}_{\mathfrak{X}, \infty}$ be its sheaf of infinite-level differential operators. A coadmissibl…

Lagrangianity conjecture. $SS(\mathcal{F})$ is an analytic Lagrangian subspace of $T^*X$, meaning that it is an analytic closed subset and is Lagrangian on its regular locus. In pa…

Microlocal endomorphism conjecture.

Slope-bound conjecture. For all $i>d$, the $q$-slopes of these eigenvalues are contained in

Torsion finiteness conjecture.

Let $X$ be a finite extension of a local nonarchimedean field, and consider the rigid analytic stack constructed in the cited work of EGH. Generalized rigid analytic stack conjectu…

Let $C$ be an algebraically closed non-archimedean field, let $A$ be a $C$-affinoid algebra, and let $n$ be an integer invertible in $\mathcal{O}_C$. Let…

Let $C$ be the base field, let $X$ be a smooth Stein rigid analytic variety over $C$, connected and of dimension $d$, and write…

Let $C$ be the completed algebraic closure of a $p$-adic field, let $\mathcal{Y}_{\operatorname{FF}}=\operatorname{Spa}(A_{\inf},A_{\inf})\setminus V([p^{\flat}])$, and let $A$ be…

Let $C$ be the completed algebraic closure of a $p$-adic field, and let $X$ be a smooth affinoid rigid space over $C$. Write $\boldsymbol{\Omega}^j(X)$ for the space of $j$-forms,…

Let $K$ be a $p$-adic discretely valued field, let $X$ be a quasi-compact and quasi-separated rigid-analytic $K$-variety of dimension $d$, let $\ell\neq p$ be a prime, and let…