On the prime spectrum of the $p$-adic integer polynomial ring with a depiction

Abstract

In 1966, David Mumford created a drawing of $\operatorname{Proj} \mathbb Z [X,Y]$ in his book, "Lectures on Curves on an Algebraic Surface". In following, he created a photo of a so-called 'arithmetic surface' $\operatorname{Spec} \mathbb Z [T]$for his 1988 book, "The Red Book of Varieties and Schemes". The depiction presents the structure of $\operatorname{Spec} \mathbb Z [T]$ as being interesting and pleasant and is a well-known picture in algebraic geometry. Taking inspiration from Mumford, we create a drawing similar to $\operatorname{Spec} \mathbb Z_p [T]$, which has a lot of similarities with $\operatorname{Spec} \mathbb Z [T]$.