5 problems

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

Optimal unitary Drinfeld uniformization conjecture. This isomorphism should be induced by an isomorphism of formal schemes over $\operatorname{Spf} O_K$,

Hamacher–Kim uniformization conjecture. For $\ell=\overline{\mathbb{F}}_p$, there should be a uniformization map

Let $(p,\mathsf G,X,\mathsf K)$ be of global Hodge type, let $x\in{\mathscr S}_{\mathsf K}(k)$, and let Condition $(U_x)$ be the condition ensuring that the abelian varieties obtai…

Let $R_\pi$ be the coefficient ring acting on the objects in the construction, let $X$ and $Y$ be the period lattices, and let $A_\Pi$ be the abelian variety attached to $\Pi$. For…