---
date: 2022-04-17 01:10
modification date: Sunday 17th April 2022 01:10:52
title: "etale fundamental group"
aliases: [etale fundamental group]
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- Course notes: <http://www.math.columbia.edu/~phlee/CourseNotes/EtaleFundamental.pdf#page=7> #resources/course-notes 
- Links:
	- #todo/create-links 

---

# etale fundamental group
![](attachments/Pasted%20image%2020221223202858.png)

![](attachments/Pasted%20image%2020220404005805.png)
![](attachments/Pasted%20image%2020220404005919.png)
See also [fiber functor](Unsorted/Tannakian.md)

![](attachments/Pasted%20image%2020220204095329.png)
![](attachments/Pasted%20image%2020220204095341.png)
![](attachments/Pasted%20image%2020220204095544.png)

Idea: $\Gal(k^\sep\slice k) \cong \pi_1^\et(\spec k, \bar{x})$ for $\bar{x}$ a [geometric point](Unsorted/geometric%20fiber.md)?

![](attachments/Pasted%20image%2020220204100150.png)

![](attachments/Pasted%20image%2020220404010029.png)

![](attachments/Pasted%20image%2020220417011034.png)


![](attachments/Pasted%20image%2020220417014327.png)

# Relation to topological fundamental group

![](attachments/Pasted%20image%2020220502184100.png)