Parabolic Fontaine-Faltings modules and parabolic Higgs-de Rham flows

Abstract: In this note, we aim to extend the concepts of the Fontaine-Faltings module and Higgs-de Rham flow to their parabolic versions. The crucial aspect of our generalization lies in the construction of parabolic inverse Cartier functors. The twisted versions discussed in Sun, Yang, and Zuo's work can be seen as a special case, where the parabolic weights are equal at every infinity point. We note that a modulo $p$ version of parabolic Higgs-de Rham flow was previously established in \cite{KrSh20} in a different way.