Random wild guess: Dumbledore has the Lost Diadem of Rowena Ravenclaw. According to canon, it enhances the wearer's wisdom, and is concealed in Hogwarts (specifically in the Room of Requirement, which either does not exist in this AU or perhaps was kept very secret by Dumledore after he found it).

We already know that Gryffindor's Sword exists in HPMOR and has special powers, and Slytherin's Locket has been alluded to, so it's plausible that Ravenclaw's Diadem is around as well.