On the Unipotent p-adic Simpson Correspondence

The goal of this paper is to show a (derived) p-adic Simpson correspondence for (locally) unipotent coefficients on smooth rigid-analytic varieties. Our results depend on a deformation to Bdr⁺/ξ², and not on a choice of exponential (as required for more general coefficients). Our methods are inherently higher categorical, hinging on the theory of modules over E_∞-algebras.