---
date: 2022-04-05 23:42
modification date: Tuesday 5th April 2022 23:42:25
title: "Shimura variety"
aliases: [Shimura variety, Shimura varieties, Shimuras]
created: 2023-04-01T09:19
updated: 2023-04-01T09:20
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- Introduction to [plectic cohomology](plectic%20cohomology) <https://webusers.imj-prg.fr/~jan.nekovar/pu/introplec.pdf#page=1> #resources/notes 
	- <https://www.youtube.com/watch?v=3ESH9URO3G4&list=PLCe-H2N8-ny6CuzEHzZshbqiuVVXIdVUe&index=3> #resources/videos 
	- [Example based introduction to Shiimura varieties](https://www-users.cse.umn.edu/~kwlan/articles/intro-sh-ex.pdf#page=1&zoom=180,-45,796)
- Links:
	- [Baily-Borel](Baily-Borel)

---

# Shimura variety

Idea: generalization of [modular curves](Unsorted/modular%20curve.md), are sometimes moduli spaces of abelian varieties with extra structure.

![](attachments/2023-03-14-5.png)

![](attachments/Pasted%20image%2020221223211055.png)


Relation to [plectic conjecture](plectic%20conjecture.md) for [motives](Unsorted/motive%20MOC.md):
![](attachments/Pasted%20image%2020220424191712.png)

Fake elliptic curves:
 
![2023-01-09-26](attachments/2023-01-09-26.png)

![](2023-04-01.png)

# Cohomology

![](attachments/Pasted%20image%2020220424191932.png)

An instance of the [plectic conjecture](plectic%20conjecture.md)
![](attachments/Pasted%20image%2020220424192002.png)