Sur la correspondance de Simpson p-adique. I : \'etude locale

TL;DR

This paper introduces a new local approach to the p-adic Simpson correspondence, inspired by Faltings and Ogus-Vologodsky, advancing understanding of p-adic local systems.

Contribution

It develops a novel local framework for the p-adic Simpson correspondence, bridging ideas from Faltings and Ogus-Vologodsky.

Findings

New local approach to p-adic Simpson correspondence

Connections established with Faltings' and Ogus-Vologodsky's work

Foundation laid for further global developments

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. This first article is devoted to the local aspects of the theory.