In Assassin's Creed, everyone's end-game is to find the Apple of McGuffin Eden.
Apparently, it either has the seeds of disobedience, or some genetic code of free-will (probably extracted with Hashashin technology from 5 centuries ago), or a mixture of these.
Sofia Rikkin wants to study it to erase violence in men. I'm guessing the idea is to study the genetic footprint and learn what genomes are linked to hereditary violence, and from there work on a human genome project to influence such genes.
Alan Rikkin, however, decides he wants to eradicate the Assassins. I don't understand that. How does the Apple allow him to do so? Why is that still relevant to the Templars, when the Assassins are all but wiped out?