I'm curious about Faltings' "A p-adic Simpson correspondence ". Do you know more detailed, introductory, expositions, surveys, texts of seminars on that?
Edit: Annette Werner's survey "Vector Bundles on Curves over C_p" seems to be related.
Edit: The first part of 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". An other related article.
Edit: today new in arxiv - "Non-abelian Hodge theory for algebraic curves over characteristic p"