A remark on the vanishing of Higgs fields in the $p$-adic Simpson correspondence

TL;DR

This paper establishes a specific condition on p-adic representations of a curve's fundamental group that guarantees the Higgs field vanishes under the p-adic Simpson correspondence.

Contribution

It provides a new criterion linking p-adic representations and Higgs fields within the p-adic Simpson correspondence framework.

Findings

Identifies a condition ensuring Higgs field vanishing

Connects p-adic representations with Higgs fields

Enhances understanding of p-adic Simpson correspondence

Abstract

We give a condition on a $p$-adic representation of the fundamental group of a curve over $\overline{\mathbb{Q}}_p$ which ensures that under the $p$-adic Simpson correspondence the Higgs field vanishes.