If a person owns a piece of land, do they own it all the way down to the core of the earth?

Once a person owns a piece of land, it is up to them to find out how to use it, including drilling down in to the earth ... Of course thel and can be owned up to the core of the earth, but at the moment, we can only reach 12 kilometers at the moment, which is the deepest hole in the earth. Whether or not you can own the land down to it's core, it depends on the landlord's choice of you digging that deep. If you are the landlord, then dig away. XD

Technically, yes. Land is the solid part of the a surface. So they would own the land until they hit liquid.