Base change of twisted Fontaine-Faltings modules and Twisted Higgs-de Rham flows over very ramified valuation rings

Abstract

In this short notes, we prove a stronger version of Theorem 0.6 in our previous paper arXiv:1709.01485: Given a smooth log scheme $(\mathcal{X}\supset \mathcal{D}{)}_{W({\mathbb{F}}_q)}$, each stable twisted $f$-periodic logarithmic Higgs bundle $(E,\theta )$ over the closed fiber $(X\supset D{)}_{{\mathbb{F}}_q}$ will correspond to a ${\mathrm{PGL}}_r({\mathbb{F}}_{p^f})$-crystalline representation of ${\pi }_1((\mathcal{X}\setminus \mathcal{D}{)}_{W({\mathbb{F}}_q)[\frac{1}{p}]})$ such that its restriction to the geometric fundamental group is absolutely irreducible.

14 pages