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arXiv · 2304.03523

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

Juan Serratos
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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 $\operatorname{Spec} \mathbb Z [T]$.

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Juan Serratos. 2023-04-07. On the prime spectrum of the $p$-adic integer polynomial ring with a depiction. https://arxiv.org/abs/2304.03523

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