A Note on Potential Diagonalizability of Crystalline Representations
  Let K_0 be a finite unramified extension of Q_p. We show that all crystalline representations of G_{K_0} (the absolute Galois group of K_0) with Hodge-Tate weights in {0, ..., p-1} are potentially diagonalizable. 
Hui Gao, Tong Liu
math.NT