Dieudonné Modules and p-Divisible Groups

The notion of `-adic Tate modules, for primes ` away from the characteristic of the ground field, is incredibly useful. The analogous notion at the prime p is that of Dieudonné modules. At finite level, Dieudonné modules classify commutative finite group schemes of p-power order over a field of characteristic p. Dieudonné modules can be used to determine the local Brauer invariant of the endomorphism algebra of a simple abelian variety over a finite field at p-adic places of the center.