41 problems

Hartl's connectedness conjecture. The space $\breve{\cal{F}}^0_b$ is arcwise connected.

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…

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…

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…

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

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…

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 $C$ 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 local field with residue field of cardinality $q$, let $X$ be a quasi-compact and quasi-separated rigid-analytic $K$-variety of dimension $d$, and let…

Let $K$ be a local field with residue characteristic $p$, let $\ell\neq p$ be a prime number, and let $\mathcal X$ be an admissible formal $\mathcal O_K$-scheme with smooth generic…

Let $K$ be a $p$-adic local field with residue field of cardinality $q$, let $X$ be a smooth proper rigid-analytic $K$-variety, let $\ell\neq p$ be a prime number, and suppose that…

Let $\mathcal{R}$ be an eigenray diagram, let $Y_\mathcal{R}$ be the non-proper scheme over the Novikov field obtained from the associated toric variety by the stated Kaliman modif…

Let $\pi_\mathcal{R}:M_\mathcal{R}\to B_\mathcal{R}$ be the symplectic fibration, let $p_\mathcal{R}:\mathcal{Y}_\mathcal{R}\to B_\mathcal{R}$ be the corresponding rigid analytic m…

Let $K$ be the coefficient field, let $m$ be a positive integer, and let $\epsilon\in(0,1)$. Let $A_K[\epsilon,1)^m$ denote the corresponding polyannulus, and let $\mathcal{E}$ be…

Let $I$ be open, let $X$ be connected and affinoid with a finite Shilov boundary, and let $\mathcal{E}$ be a regular connection of rank $n$. Suppose there are $x\in X$, a closed su…

Finiteness criterion for affinoid Liu algebras. The following assertions should hold: (i) $\calA$ is affinoid if and only if $\tilde{\calA}_{\mathrm{gr}}$ is a finitely generated…

Rigid polystable reduction conjecture. There is a rig-isomorphism $\mathcal{X}'\to\mathcal{X}$ such that $\mathcal{X}'$ is polystable.

Seminormal extension conjecture. If the space $X$ is seminormal, then the same coadmissibility and finite-projectivity result holds.