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date: 2022-02-14 10:05
modification date: Monday 14th February 2022 10:05:15
title: Hilbert symbol
aliases: [Hilbert symbol]

---

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# Hilbert symbol

![](attachments/Pasted%20image%2020220214100518.png)
For $X$ a genus zero curve:
![](attachments/Pasted%20image%2020220214100541.png)
![](attachments/Pasted%20image%2020220214100637.png)

# Quaternion algebras

See [quaternion algebra](Unsorted/quaternion%20algebra.md).
![](attachments/Pasted%20image%2020220406171431.png)

Relation to [places](Unsorted/Valuations.md):
![](attachments/Pasted%20image%2020220406171537.png)