9 problems

Let $L/\mathbb Q$ be an imaginary quadratic extension with discriminant $-D$, let $\Lambda$ be a character of $L^\times\backslash\mathbb A_L^\times$ trivial on $\mathbb A^\times$,…

Let $G=\mathrm{GSp}_4$, let $\pi=\otimes_v\pi_v$ be an irreducible, unitary, cuspidal, generic automorphic representation of $G(\mathbb A)$ with trivial central character, and let…

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…

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…

Σ × σ multiplicity-one conjecture. With these notations,

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…