URegina PIMS Distinguished Lecture: Akhil Mathew

The notion of a finite locally free group scheme is a natural generalization of the usual notion of a finite group. Lagrange's theorem states that all nth powers vanish in a group of order n. However, this need not hold for a group scheme. I will explain some history and motivation of this problem and describe a finite locally group scheme of order four (found by AI) where fourth powers are nonzero.