15 problems

Let $\operatorname{\mathfrak{X}}=(X_i)_{i\in I}$ be a formal scheme over a base scheme $S$, presented as an inductive system of schemes. Suppose that every morphism appearing in th…

Let $\operatorname{\mathfrak{X}}$ and $\operatorname{\mathfrak{Y}}$ be formal schemes over a base scheme $S$, and let…

Motivic jet-space integral conjecture. The identity

Let $Y$ be the object used to define the formally smooth deformation space $\mathbf{Def}_{\mathrm{sus}}(Y)$, and let $\mathfrak{a}_Y$ be its ambient Lie algebra. Let…

Let $X$ be a noetherian excellent $p$-adic formal scheme, and write $\operatorname{WCart}_X^{\mathrm{HT}}$ for its derived Hodge–Tate stack, namely the Hodge–Tate locus in…

Green $\delta$-form conjecture. The form $\gamma$ is a Green $\delta$-form for $Z\setminus\partial Z$ on $X\setminus\partial X$. This would extend the stated complete-intersection…

Let $(G,b,\mu)$ be a local Shimura datum and let ${\mathcal G}$ be a parahoric group scheme. Consider the local $v$-sheaf diagram … with the first map a ${\mathcal G}$-torsor and t…

Let $(G,b,\mu)$ be a local Shimura datum, let ${\mathcal G}$ be a parahoric group scheme, and let $x\in X_{\mathcal G}(b,\mu^{-1})(k)$. Local tube representability conjecture. If…

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

Integral-module conjecture. Under these hypotheses, there exists a locally free $\mathcal{O}^+$-module of finite rank on $\mathrm{Sh}_K(G,b,\mu)$ such that the conclusion of the mi…

Let $S$ be a smooth algebraic surface over a field $\Bbbk$, let $X\subset S$ be a smooth projective curve, and let $\widehat{S}$ be the formal completion of $S$ along $X$. For a si…

Let $R$ be a henselian discrete valuation ring, let $\mathscr E$ be a scheme of finite type over $R$, and let $\mathscr Y\subset\widehat{\mathscr E}_0$ be a subscheme. Write…

Let $k$ be a valued field, let $\mathfrak X$ be locally of the form $\operatorname{Spf}(\mathcal A^\circ)$ for $k$-affinoid algebras $\mathcal A$, so that $\mathfrak X$ is of finit…

Local Motivic Monodromy Conjecture. There exists a finite subset $\mathcal{S}\subset\mathbb{Z}\times\mathbb{Z}_{>0}$ such that

Monogenicity conjecture. The category $\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X)$ is monogenic.