12 problems

Let $(G,\{\mu\},b)$ be a local Shimura datum, let ${\mathcal G}$ be parahoric, set $K_0={\mathcal G}(\mathbb Z_p)$, and let $K_1$ be the kernel of the reduction map to the reductiv…

Let $(G,\mu,b)$ be an integral local Shimura datum. Denote by \mathcal{M}^{\textup{\int}}_{(G,\mu,b)} the integral model for the local Shimura variety at hyperspecial level. Repre…

Unconditional local Shimura conjecture. The natural transformation

Comparison-isomorphism conjecture. The morphism $\Upsilon^{\mathrm{sm}}$ is an isomorphism.

Bültel–Pappas conjecture. The functor

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 $G$ be a connected, quasisplit reductive group over $4p$, let $4mu$ be a dominant cocharacter, and let $b\in \mathbf{B}(G,\mu)$. Let $M_b\subset M_S\subset G$ be standard ratio…

Let $(G,[b],\{\mu\})$ be a local Shimura datum over $\mathbb{Q}_p$, with local reflex field $E$, flag variety $\mathscr{F}\ell_{G,\mu}$ over $\breve{E}$, weakly admissible locus…

Assume that $G$ is quasi-split and let $(G,[b],\{\mu\})$ be a non-basic local Shimura datum. Let $L$ be a Levi subgroup, assume that $J_b$ is an inner form of a Levi subgroup conta…

Let $(G,[b],\{\mu\})$ be a basic local Shimura datum, and let $(G^\vee,[b^\vee],\{\mu^\vee\})$ be its dual datum, with $G^\vee=J_b$, $[b^\vee]=[b^{-1}]$, and…

Let $\mathcal{D}_{\mathbb{Z}_p}$ be an integral Rapoport–Zink datum such that $[b]\in B(G,\{\mu\})$, and suppose that the group scheme $\mathcal{G}$ is parahoric. Non-emptiness con…

Let $\mathcal{D}_{\mathbb{Z}_p}$ be an integral Rapoport–Zink datum such that $\mathcal{G}$ is a parahoric group scheme. The associated rigid space is equipped with an action of…