Summary: Let $p$ be an odd prime. We show that the classification of $p$-divisible groups by Breuil windows and the classification of commutative finite flat group schemes of $p$-power order by Breuil modules hold over every complete regular local ring with perfect residue field of characteristic $p$. We set up a formalism of frames and windows with an abstract deformation theory that applies to Breuil windows.

14L05, 14F30

finite group scheme, $p$-divisible group, frame, window, deformation theory, Dieudonné display