---
date: 2022-05-03 10:57
modification date: Tuesday 3rd May 2022 10:57:15
title: period ring
aliases:
  - period ring
created: 2022-05-03T10:57
updated: 2024-01-31T14:16
---


---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

---


- https://arxiv.org/pdf/1802.03357#page=15&zoom=180,-45,463
# period ring

![](attachments/Pasted%20image%2020220512000123.png)

## The period rings
![](attachments/Pasted%20image%2020220317212651.png)
![](attachments/Pasted%20image%2020220317212728.png)

![](attachments/Pasted%20image%2020220503105658.png)
## Main properties
![](attachments/Pasted%20image%2020220318202336.png)


# Comparison theorems

See [Hodge-Tate comparison](Hodge-Tate%20comparison).
![](attachments/Pasted%20image%2020220503105935.png)

![](attachments/Pasted%20image%2020220503110036.png)

See [semistable comparison theorem](semistable%20comparison%20theorem.md)

# Examples

![](attachments/Pasted%20image%2020220410155155.png)
![](attachments/Pasted%20image%2020220410155211.png)
![](attachments/Pasted%20image%2020220410155240.png)
![](attachments/Pasted%20image%2020220410155254.png)
![](attachments/Pasted%20image%2020220410155311.png)

# Hodge-Tate

![](attachments/Pasted%20image%2020220410155332.png)
![](attachments/Pasted%20image%2020220410155351.png)