I looked into this as part of my MSc thesis. There were a few of us, and we concluded it was possible given current technology (autoflight, terrain and weather avoidance, TCAS etc).
The question which divided opinion is:
"What happens when the single pilot is incapacitated?"
We concluded that the aircraft would broadcast emergency warnings to the effect the pilot was out of action, and head for the nearest suitable airfield. This was preferred over a ground station taking control and effectively turning the aircraft into a UAV.
There were other considerations of course, such as determining that the pilot was no longer capable of flying - monitoring their health primarily. Also the consideration that the system may falsely detect an incapacitated pilot, so a means of over-riding the autonomous control.
For Cert, I suspect the only real hurdle is proving that the FMS & Autopilot would be capable of getting the aircraft safely to the ground.