I just learnt (from a comment on this blog) that Pierre Colmez hosts a wonderful page on Fontaine and Wintenberger here. I particularly recommend reading both the personal recollections of their friends and collaborators (sample quote from Mark: These \(p\)-adic Hodge theorists seemed to me like an order of monks, who were able to reveal the hidden design of a tapestry by examining it one thread at a time), as well as this article by Colmez which gives a beautiful introduction to Fontaine’s work (rather than my own somewhat superficial summary).
One can’t mention the early work of Fontaine in \(p\)-adic Hodge theory without also mentioning the recent passing of John Tate (my mathematical grandfather). Tate’s enormous contributions to mathematics are very well-known by readers of this blog, many of whom certainly knew him personally much better than me. I first met him at the 2000 Arizona Winter School, where there was an impromptu celebration for his 75th birthday. We crossed paths a few times since then, chatting about a number of things from \(p\)-adic modular forms to smoked trout (his wife made a particularly tasty version of the latter for some Harvard holiday party). I last saw him at the banquet for Barry’s 80th birthday when he called out my name in a friendly way to say hello, and I felt the flutter of satisfaction that comes when one of your idols remembers who you are. Instead of trying to write a summary of his work, however, let me instead recommend (again) that you purchase for yourself a copy of the Serre-Tate correspondence, also discussed previously on this blog.