Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.03469 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $F$ be a non-Archimedean valued field, $Σ$ a closed Riemann surface of genus at least two, and $Γ$ its fundamental group. Building on the theory of equivariant harmonic maps into $\mathbb{R}$-trees, we study the non-Archimedean Hitchin map from the $\mathrm{SL}_2(F)$-character variety $\mathcal{X}_F(Γ)$, equipped with the non-Archimedean topology, to the space of holomorphic quadratic differentials on $Σ$. We prove that this map is continuous and that its image is contained in the space of Jenkins--Strebel differentials. Moreover, we establish a dynamical characterization of unbounded representations, showing that the induced action of $Γ$ on the Bruhat--Tits tree of $\mathrm{SL}_2(F)$ is never small.