10 problems

Let $G=\operatorname{GL}_4\times\operatorname{GL}_2$, let $H=\operatorname{GL}_2\times\operatorname{GL}_2$ be embedded by $(a,b)\mapsto(\operatorname{diag}(a,b),b)$, and let…

Let $D$) be the quaternion algebra over $\mathbb{Q}$ that is non-split over $\mathbb{R}$ and $\mathbb{Q}_p$ for a prime $p$ and split at all other places. Let $G=GU_2(D)$ be the as…

Let $E\subset\overline{\mathbb{Q}_p}$ be a finite extension of $\mathbb{Q}_p$, and let $\rho:G_{\mathbb{Q}}\to\operatorname{GL}_2(E)$ be an odd continuous absolutely irreducible re…

Fix a prime number $p$. Let $F$ be a totally real field, set $g=[F:{\mathbb Q}]$, and let ${\mathfrak p}$ be a prime ideal of $F$ above $p$. Let $f_\infty$ be a Hilbert eigen newfo…

Let $F$ be a totally real field, let ${\mathcal P}$ be a place at which both quaternion algebras split, and let $G_1$ and $G_2$ be the multiplicative groups of two quaternion algeb…

Let $\mathfrak{m}$ be a maximal ideal of the Hecke algebra, with associated Galois representation $\bar{\rho}$. Let $\mathbf{F}[\mathfrak{m}]$ denote the corresponding Hecke-isotyp…

Let $Y(K_{\Sigma})$ and $Y'(K_{\Sigma})$ be a Jacquet–Langlands pair, let $\mathbf{T}$ be the relevant Hecke algebra, and let $\mathfrak{m}$ be a non-Eisenstein maximal ideal. Writ…

Clozel's conjecture. The following are equivalent:

Let ${\rm G}={\rm GL}_m(D)$ and ${\rm H}={\rm GL}_{md}(F)$, where $D$ is a central division algebra over the non-archimedean local field $F$ of reduced degree $d$. Let…

Let $S_k(N)$ be the space of Hilbert–Siegel cusp forms of weight $k$ and level $N$ on the split symplectic similitude group, let $S_k^B(N)$ be the corresponding space of algebraic…