A note on p-adic Simpson correspondence

Abstract

Given a proper smooth $p$-adic variety, we show a comparison theorem for the $p$-adic Simpson correspondence constructed by Faltings and Riemann-Hilbert correspondence constructed by Scholze. As an application we formulate a sufficient condition for ${\overline{\mathbb{Q}}}_p$-local system being de Rham. We study a $p$-adic analogue of Simpson's ${\mathbb{C}}^{\ast }$-action on the set of isomorphism classes of Higgs bundles and the corresponding Galois action on the set of isomorphism classes of generalized representations of the étale fundamental group.

34 pages