  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.
