---
date: 2022-03-17 20:51
modification date: Wednesday 23rd March 2022 16:11:29
title: Hodge F-crystal
aliases: [Hodge F-crystal, crystal, crystals, "F-crystal"]
---

Last modified date: <%+ tp.file.last_modified_date() %>


---

- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [arithmetic and 3-manifolds](arithmetic%20and%203-manifolds.md)

---

# Hodge F-crystal

![](attachments/Pasted%20image%2020220807165430.png)

![](attachments/Pasted%20image%2020220317205150.png)
![](attachments/Pasted%20image%2020220317205212.png)

See [crystalline cohomology](crystalline%20cohomology), [Gauss-Manin](Unsorted/Gauss-Manin.md), [Hodge filtration](Hodge%20filtration), [crystalline Frobenius](crystalline%20Frobenius.md).

# Misc

See [harmonic bundle](harmonic%20bundle) in [nonabelian Hodge theory](Unsorted/nonabelian%20Hodge%20correspondence.md), [local system](Unsorted/local%20system.md), [Higgs bundle](Unsorted/Higgs%20bundle.md), [Simpson correspondence](Simpson%20correspondence).

![](attachments/Pasted%20image%2020220323161116.png)
![](attachments/Pasted%20image%2020220323161127.png)
![](attachments/Pasted%20image%2020220323170402.png)

# Slopes

![](attachments/Pasted%20image%2020220807165724.png)