6 problems

Let $F$ be a local field, let $D$ be the quaternion algebra over $F$, and let $m(\rho)$ and $m(\rho_D)$ denote the multiplicities for the Ginzburg–Rallis models of $GL_6(F)$ and…

Guo–Jacquet conjecture. If $\pi_D$ is $H_D$-distinguished and $\pi$ is deduced from $\pi_D$ by the Jacquet–Langlands correspondence, then $\pi$ is $H$-distinguished.

Let $F$ be a non-archimedean local field and let $n\geq 2$. Consider the group $\operatorname{GL}_n(F)$ and the corresponding Lubin–Tate spaces of dimension $n-1$, together with th…

Let $\mathbb{G}$ be a one-dimensional formal group of finite height $n$ over a perfect field $k$ of characteristic $p$, and let $\ell$ and $p$ be distinct primes. Write $H^{n-1}$ f…

Let $G=\operatorname{GL}_r(D)$ and let $G^*=\operatorname{GL}_{rd}(F)$ be the corresponding split inner form. Write $R(G)$ and $R(G^*)$ for the Grothendieck groups of finite-length…

Let $F$ have uniformizer $c0_F$ and residue field $k$, and let $(X_m)_{m\geq 1}$ be the inverse system of Lubin–Tate curves associated with a height-$2$ formal $\mathcal{O}_F$-modu…