15 problems

Let … where the locally convex inductive limit is over open neighborhoods $U\subset N\backslash P^{\operatorname{an}}_{\operatorname{dR}}$ containing the closure of the image of…

Let $D$ be the filtered $\varphi$-module under consideration, let $\sigma$ range over the relevant embeddings, and let $I$ range over subsets that are very critical for $\sigma$. L…

Let $F$ be a finite extension of ${\mathbb Q}_p$, and let $G$ be a quasi-split group over $F$. Infinitesimal-character conjecture for quasi-split groups. Does the infinitesimal-cha…

Let $G$ be a compact $p$-adic Lie group, and let $M$ and the associated period rings and locally analytic-vector functor be as in Theorem 1. The Lie algebra $\mathrm{Lie}(G)$ is no…

Let $S\subseteq\Sigma_L$, let $I^c_S(\alpha,\mathbf h)=C(1,s_J)$ be the corresponding locally analytic representation, and let…

Breuil's conjecture. There is a natural $E$-linear bijection

Let $v\in S_p$. For each $v$, let $\widetilde v$ be the chosen place above $v$, let $\rho_{\widetilde v}$ be the associated generic potentially crystalline Galois representation, l…

Let $\rho_p:{\rm Gal}(\overline{\mathbb Q}_p/{\mathbb Q}_p)\to{\rm GL}_3(E)$ be semistable as in the preceding setup, with $\dim_E W=3$ and $N^2\ne0$. The $n=3$ local identificatio…

Let $\pi^\alpha(\rho_p)$ be the nonsplit extension attached to $\rho_p$ in the cited work, and let $\pi^\alpha(\operatorname{Fil}^{\rm \max}_\alpha(\rho_p))$ be the extension constr…

Breuil's conjecture. For a character $\chi:T(L)\rightarrow E^{\times}$,

Let $\rho$ be an $n$-dimensional continuous representation of $\operatorname{Gal}(\overline{F}/F)$ over $E$, with $\rho_{\tilde v}$ crystalline and very regular for every…

Let $G$ be a ${\mathbb Q}_p$-analytic group over $L$, and let $\Pi$ be an absolutely irreducible admissible $L$-Banach space representation of $G$. Denote by $\Pi_{\rm an}$ the spa…

Let $\mathscr{S}_*^{\mathrm{cris}}$ denote the crystalline parameter space used in the paper. For $s\in\mathscr{S}_*^{\mathrm{cris}}$ non-exceptional, let…

Let $L$ be a finite extension of ${\mathbb Q}_p$, let $\mathscr{S}_{\mathrm{irr}}$ parameterize the two-dimensional irreducible trianguline representations, and for…

Let $V$ be an irreducible crystabelian representation of $G_{{\mathbb {Q}}_p}$ with Hodge–Tate weights $(0,k-1)$ for an integer $k\geq 2$. Let $(\alpha,\beta)$ be the associated pa…