Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.06697 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913665402273792 |
|---|---|
| author | Xu, Daxin |
| author_facet | Xu, Daxin |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_06697 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parallel transport for Higgs bundles over p-adic curves Xu, Daxin Algebraic Geometry 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. |
| title | Parallel transport for Higgs bundles over p-adic curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2201.06697 |