Dualit\'{e} de Cartier et modules de Breuil

TL;DR

This paper explicitly describes the Cartier duality within the category (Mod/S) of linear algebra objects associated with finite flat O_K-group schemes, extending Breuil's anti-equivalence.

Contribution

It provides an explicit formulation of Cartier duality in the (Mod/S) category related to Breuil's classification.

Findings

Explicit description of Cartier duality in (Mod/S)

Clarification of duality correspondence in Breuil's framework

Enhancement of understanding of finite flat group schemes

Abstract

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).