5 problems

Let ${\bf G}$ be an $F$-split connected reductive algebraic group defined over $F$, let ${\bf T}$ be a maximal $F$-split torus, and let $\xi$ and $\zeta$ be the parameters used to…

Topological irreducibility conjecture. If $\sigma$ is irreducible, then $(\mathscr{N}_\sigma(\Sigma),\pi_\sigma)$ and $(B_{\sigma^*}({\EuScript {P}},V^*),T_{\sigma^*})$ are topolog…

Let $p>2$, let $K=\mathbf Q_{p^f}$, let $\overline\rho$ be a $2$-dimensional mod $p$ Galois representation, and let $R_\infty$ be a patched deformation ring with a formally smooth…

Let $G$ be a finitely generated solvable group with finite Hirsch number, where the Hirsch number is the sum … for the derived series $G_0=G$ and $G_{i+1}=[G_i,G_i]$. Shalom's conj…

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…