4 problems

Let $G$ be a definite Gross inner form, let $\mathcal{M}(G)$ be the set of $A$-shapes, and let $h(G,\varsigma;q)$ be the counting function defined from discrete global $A$-paramete…

Let $E\in\Pi^{\mathrm{alg}}(G)$ and let $\mathcal{M}(G)$ be the set of $A$-shapes. For $\varsigma\in\mathcal{M}(G)$, let $h(G,\varsigma;q,E)$ be the associated cohomological counti…

Let $G$ be a definite Gross inner form of $SO_5$ over a number field, let $p$ be a prime of the number field, let $G_p=G(\mathbb{Q}_p)$, let $\Gamma_p(q)$ be the level-$q$ $p$-arit…

Let $G$ be as above, let $\Pi^{\mathrm{alg}}(G)$ be the finite-dimensional algebraic representations of $G$, and let $\Pi^{\mathrm{coh}}(G_\infty;E)$ denote the irreducible represe…