All Questions

Let $p$ be a prime number and $\mathbb{Q}_p$ be the $p-$adic rational field. Let $E/\mathbb{Q}_p$ be a fixed finite extension. On this site, I define a finite extension $F/E$ to be "good" if ...

Let $K$ be a finitely generated field extension of $\mathbb{Q}$, and let $p$ be a prime number. Can $K$ must be embedded into a p-adic local field (i.e. a finite field extension of $\mathbb{Q}_p$) ?

There is a unique up to isomorphism algebraically closed field of characteristic 0 and cardinality of the continuum. Let's call it $K$. We usually call it $\mathbb{C}$, but by this we impose a ...

I am looking for a reference where the following result is proven: Let $k$ be an algebraically closed field. If $K$ is a complete and discretely valued field with residue field $k$. Then $K$ is one ...