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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.06697 |
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Table of Contents:
- Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric étale 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 $g\ge 2$, 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.