---
date: 2022-04-05 23:42
modification date: Tuesday 5th April 2022 23:42:25
title: geometric Langlands
aliases:
  - geometric Langlands
created: 2022-04-05T23:42
updated: 2023-12-16T00:02
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- Recommended reading: <https://sites.google.com/site/geometriclanglands2014/suggested-reading-and-references>
- Links:
	- [2021 Fargues Fontaine MOC](Projects/2021%20Fargues%20Fontaine%20MOC.md)

---

# geometric Langlands

Idea: study the [[derived moduli stack]] of [local systems](local%20systems) on an [algebraic curve](algebraic%20curve.md). More generally, consider the category of [coherent sheaves](coherent%20sheaves.md) on a curve.

![](attachments/Pasted%20image%2020220228093944.png)

![](attachments/Pasted%20image%2020220228095011.png)

![](attachments/Pasted%20image%2020220515010130.png)
![](attachments/Pasted%20image%2020220515010108.png)