What is $\Bbb Q_p(p^{1/p^\infty})$ ? I am mainly looking for a reference - i.e. which topic of number theory does this fall into?
I know what $\Bbb Q_p$ is but i don't understand the notation $p^{1/p^\infty}$ means.
Context: I am trying to understand this post.
The definition would be $\mathbb{Q}_p(p^{1/p^{\infty}}) = \bigcup \mathbb{Q}_p(p^{1/p^{n}})$, which means you adjoin all $p$-power roots of $p$. This arises in the study of (wildly) ramified extensions if you want to read about it and it is very natural to study ramification in number theory.