10 problems

Let $\bb G$ be a connected reductive group with Shimura datum $(\bb G,\bb X)$, let $\msf G$ be its relevant local base change, let $\mdc K^p$ be the prime-to-$p$ level, and let…

Let $\bb G$ be a connected reductive group over $\bb Q$ with Shimura datum $(\bb G,\bb X)$ and reflex field $E$, let $p$ and $\ell$ be primes, and let $\mdc K=\mdc K_p\mdc K^p$ be…

Let $\Gamma$ be a fixed arithmetic group, let $L$ be a coefficient lattice, and let $\{\Gamma_j\}_{j\in\mathbb{N}}$ be a family of congruence subgroups with…

Let $\phi$ be a semi-simple $L$-parameter of weakly Langlands–Shahidi type with cuspidal support $(M,\phi_{M})$. Let $\mathcal{S}(\mathbf{G},X)_{K^{p},C}$ be the corresponding Shim…

Let $(\mathbf{G},X)$ be a Shimura datum such that $G=\mathbf{G}_{\mathbb{Q}_{p}}$ is unramified, and let $K=K_{p}K^{p}$ be a sufficiently small level with…

Let $M$ and $X$ be the spaces in the paper, let $p$ be the prime under consideration, and let $k$ be as above. Write $t_p^i(M)$ for the exponent of the $p$-primary torsion in…

Let $d=2n+1$ and let $\Gamma\subset \operatorname{SO}_0(d,1)$ be an arithmetic subgroup. Let $\{\Gamma_i\}$ be a cusp-uniform sequence of torsion free congruence subgroups of…

Let $\Gamma$ be an arithmetic subgroup of $\operatorname{SL}(3,\mathbb{R})$ arising from a 9-dimensional division algebra over $\mathbb{Q}$. Let $\omega_1,\omega_2$ be the fundamen…

Let $p,q$ be odd with $p\geq q$, $p>1$, let $n=(p+q)/2-1$, and let $\widetilde X$ be the symmetric space of $\operatorname{SO}^0(p,q)$ with compact dual $\widetilde X^d$. Let $F$ b…

Let $\mathbb{G}$ be split simply connected with complex dual group $\widehat{G}(\mathbf{C})$, let $A$ be a finite-length local $W(\overline{\mathbf{F}}_p)$-algebra, and let…