4 problems

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 $K$ be a non-archimedean local field, let $G_d$ be the relevant general linear group, let $D_d^\times$ be the multiplicative group of the central division algebra of invariant…

Let $F$ be the base local field, let $K/K_3$ be unramified, and let … be embeddings such that $(\Phi_1,\Phi_2)$ is a regular semisimple pair and $(\Phi_0,\Phi_3)$ is regular semisi…

Assume the signatures of $V$ at the two archimedean places of $E_0$ are $((n-1,1),(n,0))$, so that the associated CM cycle has been defined in the relevant Lubin--Tate space. Let t…