How do I remove a false debt report on my credit rating?

I was placed in collections a few years ago for a debt that was in my ex wifes name. I was never contacted by the debt holder or given a chance to discuss it until they put me in collections. They know this is not my debt, and yet have referred me to two different collection agencies, and I recently saw that the last agency reported this on my credit report with Equifax. I was told by the collection agency they want my divorce agreement. This sounds like BS. It isnt my job to prove I dont owe the debt. It is their job to prove I do. This is fraud. What do I do about this?