8 problems

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…

Let $F$ be an imaginary CM field with maximal totally real subfield $F^+$, let $G_{/F^+}$ be the reductive group in the stated global setup, and let…

Let $K$ be a nonarchimedean local field, let $d$ be a positive integer, and let $]_{ll]}$ be the coefficient ring. Let $L]_d(K)$-representations mean representations on $]_{ll]}$-m…

Local-global compatibility conjecture. The action of $R_p^{\operatorname{loc}}$ on

Patched module conjecture. For some integer $m\geq1$, there is an isomorphism of $\overline{R}_\infty[G]$-modules

Local Langlands conjecture for $B(\chi,[1,b])$. Up to a twist by a character, $B(\chi,[1,b])$ is isomorphic to $\Pi(V_{\chi,[1,b]}^\vee)$ as a Banach space representation of…

Let $V$ be a representation in the setting of the $p$-adic local Langlands correspondence, and let $\eta,\psi\in\operatorname{Hom}_{\mathrm{cont}}({\mathbb {Q}}_p^\times,L^\times)$…

Let $V$ be a $2$-dimensional $p$-adic representation of $G_{{\mathbb {Q}}_p}$, let $\mathrm{B}(V)$ be its associated admissible unitary representation of…