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Valve: HDMI Forum Continues to Block HDMI 2.1 for Linux
(www.heise.de)
This is a most excellent place for technology news and articles.
It might be possible to get into output wirelessly, it has a dedicated radio for video output so presumably if you just stuck an adaptor into your TV you could just cast to it. Could be quite a nice setup if you wanted it to be able to connect to both your computer in the study and your TV in the living room.