Sur la r\'eduction des repr\'esentations cristallines de dimension 2 en   poids moyens
  We compute the reduction modulo $p$ of 2-dimensional crystalline representations whose Hodge-Tate weights are 0 and $k-1$ with $k \in \{p+2,...,2p-1\}$. 
Laurent Berger, Christophe Breuil