---
date: 2022-03-25 19:53
modification date: Friday 25th March 2022 19:53:40
title: filtered spectra
aliases: [filtered spectra, graded spectra, filtered ring, filtered completion, filtered, filtration, graded, grading]

---

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


---

- Tags 
	- #homotopy/stable-homotopy/equivariant
- Refs:
	- #todo/add-references
- Links:
	- [periodic sphere spectrum](periodic%20sphere%20spectrum.md)
	- [algebra over a monad](algebra%20over%20a%20monad)
	- [Day convolution](Unsorted/Day%20convolution.md)

---

# filtered spectra

Grading: ![](attachments/2023-03-04-enalg.png)

![](attachments/Pasted%20image%2020220510151908.png)

![](attachments/Pasted%20image%2020220325195342.png)

![](attachments/Pasted%20image%2020220510152128.png)

# Results
![](attachments/Pasted%20image%2020220510151456.png)

# Completion

![](attachments/Pasted%20image%2020220325202443.png)

# Spectral sequence

![](attachments/Pasted%20image%2020220527214658.png)
![](attachments/Pasted%20image%2020220527214709.png)