What brought them down? They became so big, and so powerful they posed a threat to the other powers in society. When they were richer than kings, ignored the pope, and did what they pleased, people began to worry. When the Crusaders began to lose their hold on the Holy Land, the Templars lost their major fortress in Acre in 1291, and were essentially kicked out of the Holy land. Their star bagan to fade.
On Friday, October 13, 1307 both King Philip of France and Pope Clement struck, arresting all the Templars they could round up. Charged with idolatry, heresy, corruption, and necromancy, most confessed under the questioning of the Inquisition’s torturers.
After a series of trials, appeals, and investigations, Templar Grand Master Jaques deMolay and the remaining Templars were burned at the stake in 1313. However, most of the Templars rounded up in 1307 were older knights, and nobody knows what happened to either their treasure or their extensive trading and naval fleet. Somebody obviously got them, but we don't know who.
In 2001 the Chinon Parchment from 1308 was found in the Vatican library. Someone had misplaced it in 1628, and its existence was unknown until an Italian researcher stumbled on it in 2001. It shows that in 1308 the pope declared the Templars innocent of all the accusations against them. The Church now acknowledges this.
The Prolog of The Templar Concordat takes place on October 12 and 13 of 1307.