3 problems

Let $G$ be a reductive group over a non-Archimedean field, let $\phi$ be an $L$-parameter, and let $\Pi_{\phi}^{\mathrm{ABV}}$ denote its ABV-packet. Let $\widehat{\phi}$ be the Py…

Let $F=k((t))$ be a local field, let $G(F)$ be the group of $F$-rational points, and let $\pi$ be a tempered irreducible admissible representation of $G(F)$. Let $AZ(\pi)$ be its i…

Let $G$ be a reductive $p$-adic group and let $\pi$ be an irreducible admissible representation of $G$. Define $d(\pi)$ to be the largest integer $i\geq0$ for which there is an irr…