7 problems

Let $K$ be a global field, let $\mathbf G$ be a connected absolutely almost simple $K$-group, and let $W_f$ be a compact open subgroup of $\mathbf G(\bA_f)$. For…

Temperedness conjecture. The set $\Pi_\phi$ always consists of irreducible, admissible, and tempered representations of $G(\mathbb A_F)$.

Let $k$ be a number field and let $\mathbf{G}$ be a connected, simply connected almost simple $k$-group. Theorem and Corollary assume that every local group $\mathbf{G}(k_s)$ has p…

Let $k$ be a number field, let $\mathbf{G}$ be a connected and simply connected almost simple $k$-algebraic group, and let $V$ be a unitary $\mathbf{G}(k)$-representation. Theorem…

Adelic-block conjecture. Every adelic block $G\in\mathsf{LCA}_{F}$ is both an injective and projective object.

The arithmetic-to-spectrum conjecture. The lattices $\Gamma_{K_1}$ and $\Gamma_{K_2}$ are $L$-equivalent in $G_{1,\infty}\simeq G_{2,\infty}$.

Let $F_n$ be the cyclotomic field in question, let ${\mathbb A}(F_n)$ be its ring of adeles, and let $K_{p^{n+1}-1}$ be the subgroup … of $GL(1,{\mathbb A}(F_n))$, where the produc…