In this note, we aim to extend the concepts of the Fontaine-Faltings module and Higgs-de Rham flow to parabolic versions. The crucial aspect of our generalization lies in the construction of parabolic inverse Cartier functors. The twisted versions discussed in Sun-Yang-Zuo's work can be viewed as a special case, wherein 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 by Krishnamoorthy and Sheng.PDF: Parabolic Fontaine-Faltings modules and parabolic Higgs-de Rham flows.pdf
