If Green Lantern (or any other lantern) imagines ("creates") Kryptonite

does it effect Superman?

He can and it can, but I've always imagined that it would come down to a battle of wills. Is Superman's will powerful enough to overcome the GL's ring? My answer has always been yes, but others might disagree.

They can't do that. They create constructs made of the same green stuff. Firestorm and Element Girl on the other hand, can come up with Kryptonite and slay Superman with it.

No and yes.

Green Lantern energy constructs may seem real or at least imitate real objects, but I believe there's a limit to that power. Much like if Firestorm doesn't know the atomic composition of something he cannot create it, the lanterns have the same problem. For example if they could simply recreate anything then if an enemy used a certain type of weapon that proved difficult to surpass they could simply use their rings to create a replica. But they never do it because they can't.

And although most constructs seem to recreate weapons and equipment, the weapons are made from the energy contained in their rings, and has such the damage they do depends on their willpower. If one was to imagine a nuclear missile, but hadn't the willpower to match the destructive force, then he or she could imagine it all they wanted, it wouldn't have the same effect.

So, no! They can't create kriptonite with their rings. If they could than Superboy-Prime would have been a lot more easier to defeat.

But this doesn't mean that it's impossible. It would require someone with a lot more knowledge and power, someone like a Guardian or Ion.