---
date: 2021-06-20
tags: [ web/quick-notes ]
---


# 2021-06-20

## 21:57

Tags:
#homotopy/stable-homotopy #higher-algebra/K-theory 

  - $K^\alg(\SS)$ is of interest due to Waldhausen's stable parameterized [h-cobordism theorem](h-cobordism%20theorem).
    - How to understand it: look at [Galois descent](Galois%20descent.md) on $\K(\ZZ)$
- A first approximation: $\K^\alg(L_{K(n)} \SS)$, so localize with respect to [Morava K-theory](Morava%20K-theory)
- Rognes extends [Lichtenbaum-Quillen conjectures](Lichtenbaum-Quillen%20conjectures) and develops a theory for Galois extensions of $\SS\dash$algebras

- [Redshift](Redshift) : [algebraic K-theory](algebraic%20K-theory) increases [chromatic complexity](chromatic%20complexity) by one.