I'm curious about Faltings' <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W9F-4HDGBKR-1&_user=10&_coverDate=12%2F20%2F2005&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1291551765&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=7f0cbccd03a0a56cd78627eefa1d73a4" title="sci direct">"A p-adic Simpson correspondence "</a>. Do you know more detailed, introductory,  expositions, surveys, texts of seminars on that?

Edit: Annette Werner's survey <a href="http://www.uni-frankfurt.de/fb/fb12/mathematik/ag/personen/werner/arbeiten/survey.pdf" title="pdf">"Vector Bundles on Curves over C_p"</a> seems to be related.

Edit: The <a href="http://arxiv.org/abs/1102.5466" title="link">first part</a> 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". <a href="http://hal.archives-ouvertes.fr/docs/00/33/76/72/PDF/Higgs.pdf" title="link">An other related article</a>.

Edit: today new in arxiv - <a href="http://de.arxiv.org/abs/1306.0299" title="pdf">"Non-abelian Hodge theory for algebraic curves over characteristic p"</a>