4 problems

For each integer $m\geq 0$, let $\Pi_m$ and $\pi_m$ be the maps defined in the paper from the Ekedahl–Oort stratification data. Independence conjecture. The maps $\Pi_m$ and…

Correspondence conjecture. The smooth loci of ${\mathcal U}$ and ${\mathscr U}_{\mathbb C}$, respectively the normal loci of ${\mathcal U}$ and ${\mathscr U}_{\mathbb C}$, correspo…

Let $G$ be a reductive group over the relevant local field, let $K$ be a $sigma$-stable hyperspecial subgroup containing an Iwahori subgroup $I$, and let $mu$ be a noncentral cocha…

Let $G$ be a reductive group, let $mu$ be a Hodge cocharacter, and let $K$ be a parahoric subgroup. Assume that $(G,\mu,K)$ is of Coxeter type, and let the corresponding basic affi…