9 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 $(G,b,\mu)$ be a local Shimura datum, with $G$ a reductive group over $\mathbb{Q}_p$, $b\in G(\breve{\mathbb{Q}}_p)$, and $\mu$ a minuscule conjugacy class of cocharacters, and…

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…

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

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