Lexus has built a hoverboard

The BBC has an article by Vijay Pattni about an implausible invention:

Lexus has revealed it is working on a prototype hoverboard. If you are familiar with a particular movie of the late 1980s, this should make you deliriously happy.
Lexus' project team has collaborated with "experts in super-conductive technology" to build an actual, working, real-life hoverboard. No joke; they tell us the team is using magnetic levitation with liquid nitrogen-cooled super-conductors and permanent magnets to "give the hoverboard frictionless movement of a kind that had been thought impossible". Impossible? Not unless you've watched Back to the Future II several times.
Lexus tells us the hoverboard shares some design cues with the current Lexus range of cars, including that Predator-style spindle grille. It apparently features materials sourced from Lexus' road car range, though whether it'll boast a curiously old-school digital clock remains unclear.
The hoverboard is planned as a one-off, sadly, and won't be put up for sale. But who cares? They'll be testing the prototype in Barcelona, Spain over the next few weeks, ahead of a summer launch.
Check the video to see a teaser of the technology in action: a teaser, admittedly, that doesn't show a whole lot in the way of hovery, skatey action.
But that's fine, because they've got until 21 October 2015 to get it all ready. Now, all we need is a flying DeLorean and a flux capacitor...

Rico says he'll wait for the explanation of how this works; gravity is a bitch to overcome...