Sch\'emas en groupes et poids de Diamond-Serre

Abstract

This note is a correction of (statement and proof of) proposition 3.3.1 of Toby Gee's preprint intitled *On the weights of mod p Hilbert modular forms*. The aim is to compare Galois representations arising from extensions of some group schemes (over the ring of integers of a p-adic field) endowed with a descent data, and extensions of some crystalline representations with given Hodge-Tate weights. The main tool of the proof is the theory of Breuil.