15 problems

Cohomological smoothness conjecture. The structure morphism

Let $L_0=\mathbb Z_p^n$ and $L_0^\vee=p^{-1}\mathbb Z_p^t\oplus\mathbb Z_p^{n-t}$, and let $\mathrm{GL}(L_0,L_0^\vee)$ be the corresponding parahoric subgroup. For a regular semisi…

Let $0\leq r\leq n+1$, let $\varepsilon$ be the parity of $r$, and let $W_\varepsilon$ and $W_{\varepsilon+1}$ be the hermitian spaces of dimension $n+1$ with opposite invariants.…

For $0\leq r\leq n$, let $\widetilde{\mathcal{N}}^{[r]}_n$ be the formal scheme constructed from the relevant Rapoport--Zink spaces, and let $p$ be the residue characteristic. Regu…

Arithmetic transfer conjecture for odd type $(r,0)$. There exists $\varphi'\in C_c^\infty(G')$ transferring to $(c_r^2\\,\mathbf{1}_{K_n^{[r]}\times K_{n+1}},0)$ such that, for eve…

Let $t\neq t'$ and let $A$ be any closed formal subscheme of the Rapoport–Zink space $\mathcal{N}_n$. The correspondence $\mathcal{T}_n^{\leq t}$ is obtained by composing the corre…

Let $(\mathrm{G},b,\mu)$ be a PEL-type Rapoport–Zink datum, with $\mathrm{G}$ a connected reductive group over $\mathbb{Q}_p$, $\mu$ a minuscule cocharacter, and…

Let $(G,b,\mu)$ be the local Shimura data appearing in the paper, let $\mathcal{H}^{\mathfrak{e}}$ be an endoscopic datum, and let $\operatorname{Mant}_{G,b,\mu}$ and…

Let $(G,\mu)$ be a local Shimura datum as in the source, let $b\in\mathbf{B}(G,\mu)$, and let $M_S\subset M_b$ be a standard Levi subgroup. Let $\rho$ be a supercuspidal representa…

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…

Let $S(E_0)$ be the relevant symmetric space, let $U(J_1)$ be the unitary group attached to the odd hermitian form, and let $Ω(γ)$, $\partial O_γ(1_{S(\mathcal{O}_{E_0})})$, and…

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…