Cartier duality for $(ϕ, \hat{G})$-modules

Dualité de Cartier et modules de Breuil

Let O\_K be a complete discrete valuation ring. Denote by K its fractions field and by k its residue field. Assume that k is of characteristic p>0 and perfect. Breuil gives an anti-equivalence between the category of finite flat O\_K-group schemes killed by a power of p and a category of linear algebra objects which is called (Mod/S). The aim of this article is to make explicit the Cartier duality on the category (Mod/S).