14 problems

Let $G$ be the group under consideration, let $F$ be the underlying number field, and let $\pi=\pi_\infty\otimes\pi_f$ be an automorphic representation of $G(\mathbb A)$. For a spl…

Among automorphic representations of $\operatorname{GSp}(4)$, Saito–Kurokawa lifts provide genuine non-tempered examples, but they are non-generic. Generalized Ramanujan conjecture…

Let $U\subset\mathcal{W}\times\mathcal{W}$ be a 2-dimensional affinoid parameterising a Coleman family $\underline{\pi}$ for $\operatorname{GSp}_4$, let $U'\subset\mathcal{W}$ be a…

Let ${\mathcal S}$ be a set of types, and let $\mathrm{JH}(\overline{\sigma}({\mathcal S}))$ be the union of the Jordan--Hölder factors of the reductions…

Let ${\mathcal X}_{{\mathrm{Sym}},K,\mathrm{red}}$ be the reduced Emerton--Gee stack, and let ${\mathcal Z}_{\lambda,\tau}$ be the $4f$-dimensional cycle attached to a regular Hodg…

Let $G_K$ be the absolute Galois group of $K$, let $\overline{\rho}:G_K\rightarrow\mathrm{GSp}_4(\mathbf{F})$ be continuous, and let $R_{\overline{\rho}}^\square$ be its framed def…

Let $A/\textbf{Q}$ be a modular abelian surface, let $\pi$ be the associated automorphic representation of $\operatorname{GSp}_4/\textbf{Q}$, and let $p$ be a prime. Say that $\pi$…

Novodvorsky compatibility conjecture. We have

Let $F$ be a totally real field, let $p$ be a prime split completely in $F$, and let $\overline{\rho}:G_F\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ be a mod $p$ irreduci…

Let $k$ be a number field with adele ring ${\mathbb A}_k$, let $G$ be a connected reductive linear algebraic group over $k$, and let $\pi=\bigotimes_v\pi_v$ be an irreducible cuspi…

Let $F$ be the totally real field and $D$ the quaternion algebra used to define $\mathrm{PGU}_2^D$. Let ${\mathscr A}_{\mathrm{cusp}}(\mathrm{PGU}_2^D)$ denote the space of cuspida…

Non-genericity conjecture. Such CAP forms are never generic.

Let $\rho:G_{\mathbb{Q}}\longrightarrow GSp_4(\mathbb{C})$ be a symplectically odd Artin representation whose image does not factor through, up to conjugacy in $GSp_4(\mathbb{C})$,…

Serre-weight conjecture. (i) The set ${\cal W}(\overline{\rho})$ is nonempty and