All Questions

Let $n \in \mathbb{N}$, $K$ a (nonarchimedean) local field, $\overline{K}$ its algebraic closure. Take a compact subgroup $G \leq \text{GL}_n(\overline{K})$. Must there be a finite extension $F$ of $K$...

For a finite group, there are finitely many irreducible representations of complex numbers. What if the field is changed to some other fields? Like real numbers, p-adic field, finite field? In ...