The main trekking routes in Corsica run through the national park, where wild camping isn't allowed. Elsewhere on the island, technically you should ask permission, but when you're faced with rocky mountainsides covered in dense maquis, it isn't at all clear who you should ask. Having said that, wild camping DOES take place, and unfortunately too many people do it in a very visible manner, leaving scorched earth and rubbish behind them. If you can do it discreetly, then no-one will even know you are there. The popular beaches aren't suitable for wild camping, by the way. Some of the quieter ones aren't suitable for lazing either, since they often involve tough walking to reach.