3 problems

Let $G=GL_2(F)$), let $C$ be as in the source with ring of integers $\mathcal{O}_C$, and let $\Theta_{\underline{k},a}$ be the $\mathcal{O}_C[G]$-lattice in $\Pi_{\underline{k},a}$…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $C$ be a sufficiently large finite extension, let $G=GL_2(F)$, and let $S$ be the set of embeddings of $F$ into $C$. For…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $C$ be a sufficiently large finite extension of $\mathbb{Q}_p$, and let $G=GL_n(F)$. Let $D$ be the filtered $(\phi,N)$-module…