Finite Group Schemes over Bases with Low Ramification

Abstract

Let A$^′$be a complete characteristic (0,p) discrete valuation ring with absolute ramification degree e and a perfect residue field. We are interested in studying the category${\mathcal F}$${\mathcal F}$$_A$$_′$of finite flat commutative group schemes over A$^′$withp-power order. When e= 1, Fontaine formulated the purely ’linear algebra‘ notion of a finite Honda system over A$^′$and constructed an anti-equivalence of categories between${\mathcal F}$${\mathcal F}$$_A$$_′$and the category of finite Honda systems over A$^′$ when p< 2. We generalize this theory to the case e≤ − 1.