Breuil modules for Raynaud schemes Original Research Article

Breuil modules for Raynaud schemes Original Research Article Pages 2939-2950 David Savitt Close Close preview | Purchase PDF (193 K) | Related articles | Related reference work articles AbstractAbstract | ReferencesReferences Abstract Let p be an odd prime, and let image be the ring of integers in a finite extension image. Breuil has classified finite flat group schemes of type (p,…,p) over image 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 image over image. When image has rank one, the generic fiber of image corresponds to a Galois character, and we explicitly determine this character in terms of the Breuil module of image. Special attention is paid to Breuil modules with descent data corresponding to characters of image that become finite flat over a totally ramified extension of degree pd−1; these arise in Geeʹs work on the weight in Serreʹs conjecture over totally real fields. Video abstract For a video summary of this paper, please visit http://www.youtube.com/watch?v=9oWYJy_XrZE.