IIRC there is no material we're aware of that has anywhere near enough compressive strength to build that high, regardless of how wide the base is. Space eleva

IIRC there is no material we're aware of that has anywhere near enough compressive strength to build that high, regardless of how wide the base is. Space elevators only (theoretically) work because the entire structure is in tension. And the only material we currently know of that can handle the tensile forces is carbon fiber.