BREUIL O-WINDOWS AND π-DIVISIBLE O-MODULES

Let p > 2 be a prime number. Let O be the ring of integers of a finite extension of Q(p) and let p be a uniformizer of O. We prove that, for any complete Noetherian regular local O-algebra R with perfect residue field of characteristic p, the category of Breuil O-windows over R is equivalent to the category of p-divisible O-modules over R. We also prove that the category of Breuil O-modules over R is equivalent to the category of commutative finite flat O-group schemes over R which are kernels of isogenies of p-divisible O- modules. As an application of these equivalences, we then prove a boundedness result on Barsotti-Tate groups and deduce some corollaries. The results generalize some earlier results of Zink, Vasiu-Zink, and Lau.