Pointwise criteria of p-adic local systems
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908096256802816 |
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| author | Guo, Haoyang Yang, Ziquan |
| author_facet | Guo, Haoyang Yang, Ziquan |
| contents | Given a Z_p-linear local system over a smooth rigid space, we show that it is crystalline (resp. semi-stable) with respect to any smooth (resp. semi-stable) integral model if and only if its restrictions at many classical points are crystalline (resp. semi-stable) representations. To this end, we introduce a crystalline Riemann--Hilbert functor, and give several applications, including a semi-stable comparison theorem in the relative setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19742 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pointwise criteria of p-adic local systems Guo, Haoyang Yang, Ziquan Algebraic Geometry Number Theory 14F30, 14G45 Given a Z_p-linear local system over a smooth rigid space, we show that it is crystalline (resp. semi-stable) with respect to any smooth (resp. semi-stable) integral model if and only if its restrictions at many classical points are crystalline (resp. semi-stable) representations. To this end, we introduce a crystalline Riemann--Hilbert functor, and give several applications, including a semi-stable comparison theorem in the relative setting. |
| title | Pointwise criteria of p-adic local systems |
| topic | Algebraic Geometry Number Theory 14F30, 14G45 |
| url | https://arxiv.org/abs/2409.19742 |