Dieudonné theory for Faltings' strict ϭ-modules

Abstract

The theory of group schemes and their liftings to mixed characteristic valuation rings is well-developed. In [Fal02], a new equi-characteristic analogue of group schemes, known as group schemes with strict ๕-action, or strict ๕-modules, was proposed and developed, including Dieudonné theory. In [Abr04], their theory was studied over a complete discrete valuation ring. In this Thesis, a version of Dieudonné theory is developed for the strict ๕-modules of [Abr04] over a perfect field, using constructions of [Fon77], using very different methods from those deployed in [Fal02]