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

TL;DR

This paper provides a comprehensive overview of the development of the p-adic Simpson correspondence, integrating ideas from Faltings, Ogus, and Vologodsky, covering both local and global theories.

Contribution

It synthesizes and reviews the extensive theory of the p-adic Simpson correspondence developed across two articles, highlighting its foundational aspects and connections.

Findings

Extensive overview of p-adic Simpson correspondence theory

Integration of local and global perspectives

Connections to characteristic p>0 analogues

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.