5 problems

Global Gan–Gross–Prasad conjecture. Let $\pi$ and $\pi^\prime$ be irreducible tempered cuspidal automorphic representations of $\operatorname{GSpin}(W)(\mathbb{A})$ and…

Let $(G,H)$ be one of the smaller models $(\operatorname{GSpin}_{10}\times\operatorname{GSpin}_3,\operatorname{GSpin}_3\ltimes U)$,…

Let $G=\operatorname{GSp}_4\times\operatorname{GL}_2\times\operatorname{GL}_2$ with $H=(\operatorname{GL}_2\times\operatorname{GL}_2)^0$, let $(G_D,H_D)$ be its quaternionic inner…

Strong generic Arthur packet conjecture. If $\Pi(\phi_{\psi})$ has a generic member, then $\Pi(\phi_{\psi})$ is a tempered $L$-packet; equivalently, all members of…

Weak generic Arthur packet conjecture. If $\Pi(\phi_{\psi})$ has a generic member, then the Langlands parameter $\phi_{\psi}$ is tempered.