6 problems

Functoriality conjecture. The representation

Rigid refined local Langlands conjecture. There is a bijection, depending on $\mathfrak{w}$,

Let $A$ act on the rigid inner twists of a connected reductive group $G$, on tempered refined Langlands parameters, and on the set $\Pi_{\mathrm{temp}}$ of tempered representations…

Kottwitz's multiplicity conjecture. The multiplicity of $\pi$ in the discrete spectrum of $G$ is given by

Let $F_v$ be a local completion of the global function field $F$, let $G$ be a connected reductive group over $F_v$, and let $W_{F_v}'$ be the Weil–Deligne group. For a tempered…

Let $G^{*}$ be a connected, reductive, quasi-split group over the local function field $F$, with finite central $F$-subgroup $Z$, and let $G$ be an inner form of $G^{*}$. Fix a Whi…