---
date: 2022-04-05 23:42
modification date: Thursday 12th May 2022 16:46:33
title: "Milnor Conjecture"
aliases: [Milnor Conjecture, "Milnor conjecture", "norm residue isomorphism"]
---

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

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [algebraic K theory](Unsorted/K-theory.md)
	- [motives](Unsorted/motive%20MOC.md)

---

# Milnor Conjecture

Statement: there is an isomorphism
\[
\KM_n (k) /\ell \to H_\et^n(k, \mu_\ell^{\tensor n} )
\]
Taking $\ell = 2$ is the Milnor conjecture.

![attachments/Pasted image 20211017151340.png](attachments/Pasted%20image%2020211017151340.png)