---
date: 2022-02-23 18:45
modification date: Wednesday 23rd February 2022 18:45:08
title: Riemann-Hilbert correspondence
aliases: [Riemann-Hilbert correspondence, Local systems biject with monodromy representations]

---

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


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- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [Verdier duality](Verdier%20duality)
	- [Grothendieck duality](Grothendieck%20duality)
	- [perverse t-structure](perverse%20t-structure.md)
	- [D modules](Unsorted/D%20modules.md)
	- [perverse t-structure](perverse%20t-structure)
	- [Simpson correspondence](Simpson%20correspondence)
	- [nearby cycle](Unsorted/vanishing%20cycles.md)

---

# Riemann-Hilbert correspondence

![](attachments/2023-03-12RH.png)

![](attachments/Pasted%20image%2020220515004745.png)

![](attachments/Pasted%20image%2020220502184520.png)

![](attachments/Pasted%20image%2020220323172204.png)
![](attachments/Pasted%20image%2020220323172218.png)

![](attachments/Pasted%20image%2020220221005919.png)

![](attachments/Pasted%20image%2020220330203518.png)



# Local systems biject with monodromy representations

![](attachments/Pasted%20image%2020220430152900.png)

# Local systems biject with flat vector bundles

![](attachments/Pasted%20image%2020220502135936.png)
![](attachments/Pasted%20image%2020220502140012.png)