Wouldn't a hoverboard with rockets on the bottom and back work? I'm not saying it's feasible, just that it's utilizing the same basic science as jets and space travel.
I think if you look up the smallest rocket that is capable of even lifting you off the ground on an instantaneous basis, let alone over time, you are going to be somewhat surprised at the size. I think you will also decide you don't particularly want to be at point-blank range to this rocket when it goes.
I mean, theoretically, if you loosen the definition of "hoverboard" enough, it might be possible to create something that hovers with you on it, but I don't think you'd accept it as a substitute for the movie hoverboard.
