10 problems

Iwahori-restriction conjecture. If $\pi\in\mathfrak{Rep}^{\textnormal{ladm}}(G)$ is injective, then

Compact-subgroup injectivity conjecture. If $\pi\in\mathfrak{Rep}^{\textnormal{ladm}}(G)$ is injective, then $\pi|_K$ is injective in $\mathfrak{Rep}^\infty(K)$. Consequently,

Effaceability conjecture. The functors $\textnormal{H}^i\textnormal{Ord}^G_{P^-}$ are effaceable on $\mathfrak{Rep}^{\textnormal{ladm}}(G)$ for $i>0$. Consequently,

Let $I,J\subseteq\Delta$, let $\sigma$ be a locally admissible smooth representation of $L_I$ over $A$, let ${}^Iw^J\in{}^IW^J$, and let $n\in\mathbb{N}$. Let $d_{{}^Iw^J}$ and…

Let $W$ be the Weyl group of $(\mathbf{G},\mathbf{S})$, let $I,J\subseteq\Delta$, let $\sigma$ be a locally admissible smooth representation of $L_I$ over $A$, let…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $G$ be a connected reductive group over $F$, and let $P\subset G$ be a standard parabolic subgroup with standard Levi subgroup…

Emerton's conjecture. Le morphisme

Let $\overline{r}:{\operatorname{Gal}}(\overline F/F)\rightarrow {\operatorname{GL}}_n(k_E)$ satisfy the three conditions stated in the source:…

Let $r:{\operatorname{Gal}}(\overline F/F)\rightarrow {\operatorname{GL}}_n(E)$ be continuous, satisfy conditions (i)–(iv) stated in the source, and suppose that for a compact open…

Let $\overline{r}:{\operatorname{Gal}}(\overline F/F)\rightarrow {\operatorname{GL}}_n(k_E)$ be continuous and absolutely irreducible, assume that $\overline{r}$ is modular and tha…