6 problems

Let $\theta$ be a stable grading on the dual Lie algebra $\widehat{\mathfrak g}$, with associated parahoric subgroup $P$. Let $p:\widehat{\mathfrak g}_1\to\widehat{\mathfrak g}(1)$…

Let $G$ be a connected reductive group over the maximal unramified extension of a non-archimedean local field, let $G_r$ be the truncated parahoric group scheme associated to a poi…

Assume ${\bf G}_{\mathbb Q_{p^r}}$ is unramified and $K_p\subset{\bf G}(\mathbb Q_p)$ is parahoric. Let $d={\rm \dim}(Sh_{K_p})$, and let $z_{-\mu,j}$ be the Bernstein function asso…

Vertexwise admissibility conjecture. The inclusion

Assume the setup of a parahoric group scheme $\mathcal G$ over a curve $X$ and let $\mathcal M_{\mathcal G/X}$ denote the moduli stack of $\mathcal G$-torsors. Let $x\in X(k)$, let…

Assume that $\operatorname{char}(k)\neq 2$, that $\pi:\widetilde X\rightarrow X$ is a possibly ramified double cover with involution $\sigma$, and set…