---
date: 2022-01-26 10:03
modification date: Wednesday 9th February 2022 10:12:53
title: Arakelov
aliases: [Arakelov divisor, Arakelov theory]

---

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# Arakelov

Idea: formulate algebraic geometry over some compactification of $\spec \ZZ$.
# Arakelov divisor

![](attachments/Pasted%20image%2020220126100340.png)
![](attachments/Pasted%20image%2020220126100559.png)
![](attachments/Pasted%20image%2020220126100432.png)
![](attachments/Pasted%20image%2020220126100525.png)

See [principal divisor](principal%20divisor), [picard group](Unsorted/class%20group.md), [place](place).