---
date: 2022-03-15 17:58
modification date: Tuesday 15th March 2022 17:58:11
title: six functor formalism
aliases: [six functor formalism]

---


---

- Tags 
	- #todo/untagged
- Refs:
	- <http://www.math.titech.ac.jp/~shanekelly/EtCohNotes7.pdf#page=2> #resources/summaries 
- Links:
	- [condensed math](Projects/2020%20Condensed%20Mathematics.md)
	- [[proper base change]]

---

# six functor formalism
![](attachments/Pasted%20image%2020220516191730.png)
![](attachments/Pasted%20image%2020220516191912.png)



![](attachments/Pasted%20image%2020220413184130.png)

Should involve [Verdier duality](Verdier%20duality), [projection formula](projection%20formula), [Poincare duality](Poincare%20duality), [proper base change](proper%20base%20change).
Involves [separated](Unsorted/separated.md) [finite type](Unsorted/finite%20type.md) schemes.
![](attachments/Pasted%20image%2020220319190046.png)
![](attachments/Pasted%20image%2020220315175815.png)


Problem: [QCoh](Unsorted/quasicoherent%20sheaf.md) doesn't quite admit such a formalism:
![](attachments/Pasted%20image%2020220319190227.png)

Used for [etale cohomology](Unsorted/l-adic%20cohomology.md):
![](attachments/Pasted%20image%2020220516192256.png)