All Questions

It is easy to prove that for a an irreducible polynomial $P$ of degree $d$ of $\mathbb F_q[T]$, one can embed $\mathbb F_{q^d}$ in $\mathbb F_q(T)_P$ (the completion of $\mathbb F_q(T)$ at $P$) and ...

I need a reference to the following claims which, I believe, are correct and well known to experts (I am not one of them). Let $K$ be a non-Archimedean local field. Let $\mathcal{O}$ be its ring of ...

This may be well known, but I was unable to find an answer browsing literature. Let us temporarily call a commutative (unital) ring $R$ an O-ring if there exists an integer $n \ge 1$, a local field of ...