Frames and finite group schemes over complete regular local rings

TL;DR

This paper extends the classification of p-divisible groups and finite flat group schemes to complete regular local rings with perfect residue fields of characteristic p, using a formalism of frames and windows.

Contribution

It generalizes existing classifications by employing a new formalism of frames and windows with an abstract deformation theory applicable to Breuil windows.

Findings

Classification of p-divisible groups by Breuil windows holds over these rings.

Finite flat group schemes of p-power order are classified by Breuil modules in this setting.

The formalism simplifies understanding of deformation theory for these structures.

Abstract

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