Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric & eacute;tale fundamental group of a smooth proper p-adic curve X are equivalent to semi-stable Higgs bundles of degree zero over X. In this article, we establish, over a p-adic curve of genus g >= 2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g\ge 2,$$\end{document} an equivalence between these representations and Higgs bundles, whose underlying bundles potentially admit a strongly semi-stable reduction of degree zero. We show that these Higgs bundles are semi-stable of degree zero and investigate some evidence for the aforementioned conjecture.

Publication:

MATHEMATISCHE ANNALEN

http://dx.doi.org/10.1007/s00208-026-03470-0

Author:

Xu, Daxin(corresponding author)

Chinese Acad Sci, Morningside Ctr Math, Beijing 100190, Peoples R China

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Email address:daxin.xu@amss.ac.cn