Let $\mathcal{O}_L = \mathbb{Z}[\sqrt{-5}]$ be the number ring of $L=\mathbb{Q}[\sqrt{-5}]$, and $\mathfrak{p} =(2, 1+\sqrt{-5})$ a prime (and maximal ideal) in $\mathcal{O}_L$.
What is the inverse (projective) limit of the following,
$$\mathcal{O}_{L,\mathfrak{p}} = \lim\substack{\leftarrow \\ n} (\mathcal{O}_L /\mathfrak{p}^n).$$
I think it is $\mathcal{O}_L$ but this is purely intuition.