iPhone, Gmail and automatic message deletion

I set up my Gmail account on my iPhone 4S. It does some weird things like downloading 500 spam messages to my phone automatically, which I really don't need. But my main question is that when I delete a message on my phone from the Gmail account, it also deletes it from my main computer. How can I change this? I like to keep emails on my laptop, but delete duplicates on my iPhone. I don't want to delete them entirely. I found no setting in the iPhone or in my Apple Mail that controls this. Generally I don't know if the control of this is on my laptop, on my iPhone, or somewhere in Gmail, and how to change it.

Thank you.