Sur la correspondance de Simpson p-adique. I : \'etude locale
  We develop a new approach for the p-adic Simpson correspondence, closely related to the original approach of Faltings, but also inspired by the work of Ogus and Vologodsky on an analogue in characteristic p>0. This first article is devoted to the local aspects of the theory. 
Ahmed Abbes and Michel Gros
math.AG math.NT