# The Going Down Theorem

Idea: for $A$ a normal domain and $f: A\to B$ an integral extension, $f^\sharp: \spec B\to \spec A$ is an open map.
# Statements

![Statement of the going down theorem](attachments/Pasted%20image%2020220114184528.png)
![Pasted image 20220114184615.png](Pasted%20image%2020220114184615.png)
![](attachments/Pasted%20image%2020220120131243.png)

## Proof
![Proof of the going down theorem](attachments/Pasted%20image%2020220114184542.png)