By default, AC4 on the PS4 will run at 900p, with an update needed in order to bring it up to 1080p.
According to AC4’s associate producer, Sylvain Trottier, most people will not even notice the difference between the two settings. 1080p for the game had been delayed because Ubisoft wanted to make sure that the game could run at a steady 30fps before the PlayStation 4 was released. Since then, they have been continually working on refining the game and bringing it up to the desired resolution. [UbiBlog]