All Questions

I'm taking a shot in the dark with this question, so I apologize if it makes no sense. Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $K_n$ be the field obtained by adjoining the $n$-th ...

Let $K$ be a finite extension of $Q_p$. Let $q$ be the size of the residue field of $K$, and let $\pi$ be a uniformizer of $K$. Then $q/\pi$ is some power of $\pi$ up to a unit $u$ in $K$, say $q/\pi =...

Let $K/F$ be a finite extension of local fields (of characteristic 0). Is it true that the quotient group $K^\times/ F^\times$ is always compact? I understand that if the extension is cyclic, it is ...

Let $P$ be a an irreducible polynomial of $k:=\mathbb F_q(T)$, $\Omega_P$ be the completion of an algebraic closure $\overline{k_P}$ of $k_P$, the completion of $k$ for the topology induced by the $P$-...

I started to read Colin Bushnell's notes on this title. The last theorem in the 3rd section claims that if $\pi$ is an irr. smooth rep. of $GL_N(F)$ containing a non-split fundamental stratum, then $\...