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.