The biggest question to be answered is, who owns it?
Just because you found something does that mean that you have every right to do what you want with it?
If you dig up artifacts in a different part of the world do you take it home? or does the place where you dug it up have the right to it? or do the artifacts belong to the country of origin?
If everyone already knows about it, but you dig it up, does that mean you have more say in what happens to it over everyone else?
What are the boundaries when it comes to digging up graves and removing bodies?
Laws have been made in an attempt to navigate this hazy area. In America the Society for American Archeology states that “except for materials on federal land, state law applies and, with some exceptions, objects are the property of the land owner.” But there is not fixed rule on the subject and it will be different in different states.
However, like everything, regardless of laws people will still take what they want and do what ever they want with those things even if it could be valuable to a cultures history.