An overview

Initiated by Faltings [18] and developed following different approaches including those by Tsuji and by the authors [3], the p-adic Simpson correspondence provides an equivalence of categories between certain p-adic étale local systems over an algebraic variety defined over a p-adic field and certain Higgs bundles. The key idea behind its construction comes from Faltings’ approach in p-adic Hodge theory, more precisely from his strategy for the computation of the cohomology of a p-adic etale local system.