Breuil modules for Raynaud schemes

Let p   be an odd prime, and let OKOK be the ring of integers in a finite extension K/QpK/Qp. Breuil has classified finite flat group schemes of type (p,…,p)(p,…,p) over OKOK in terms of linear-algebraic objects that have come to be known as Breuil modules. This classification can be extended to the case of finite flat vector space schemes GG over OKOK. When GG has rank one, the generic fiber of GG corresponds to a Galois character, and we explicitly determine this character in terms of the Breuil module of GG. Special attention is paid to Breuil modules with descent data   corresponding to characters of Gal(Q¯p/Qpd) that become finite flat over a totally ramified extension of degree pd−1pd−1; these arise in Gee's work on the weight in Serre's conjecture over totally real fields.Video abstractFor a video summary of this paper, please visit http://www.youtube.com/watch?v=9oWYJy_XrZE.