Sur la correspondance de Simpson p-adique. 0 : une vue d'ensemble

Abstract

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. The aim of this article is to give an extensive overview of the theory that has been developped in two articles, the first one (arXiv:1102.5466) devoted to the local aspects and the second one (arXiv:1301.0904) to the global aspects.

in French ; an English version will appear in the volume 193 of Annals of Mathematics Studies (PUP) edited by A. Abbes, M. Gros and T. Tsuji; some minor modifications have been made following an improvement in arXiv:1107.2380