Sur la correspondance de Simpson p-adique. II : aspects globaux

TL;DR

This paper advances the p-adic Simpson correspondence by exploring its global aspects, building on Faltings' approach and inspired by Ogus and Vologodsky's work in characteristic p>0.

Contribution

It introduces a new global perspective on the p-adic Simpson correspondence, extending previous local theories and integrating ideas from characteristic p>0 studies.

Findings

Development of a global framework for p-adic Simpson correspondence

Connections established with Ogus and Vologodsky's characteristic p>0 work

Enhanced understanding of p-adic Hodge theory

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 second article is devoted to the global aspects of the theory.