5 problems

Let $Sh_{K_p}$ be a PEL Shimura variety with standard parahoric level subgroup $K_p$, and let … be the map sending a point to the $c3$-conjugacy class of its associated isocrystal.…

Let $k$ be an algebraically closed field of characteristic $p$, and let $S$ be a PEL type Shimura variety over $k$. For a point $x\in S$, let its prime-to-$p$ Hecke orbit be the or…

Let $G$ be unramified over $\mathbb Q_p$, let $K=K_pK^p$ be hyperspecial at $p$, and let $\Theta:\mathscr{S}_K(G,X)(\kappa(\wp))\to B(G)$ be the Newton-point map. Define … The Newt…

Let $G=SL_n(F)$, let $x=\pi^{\mu}w\in\widetilde{W}$, and suppose that $\mu$ is dominant, meaning … for every simple root $\alpha_i$ in $\operatorname{Lie}(G)$, equivalently…

Let $G$ be the group under consideration, let $x\in\widetilde{W}$ be an element of its affine Weyl group, and let $b\in G$. Let $I$ be an Iwahori subgroup, let $X_x(b)$ be the asso…