Prismatic crystals and $p$-adic Riemann--Hilbert correspondence
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912136221949952 |
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| author | Gao, Hui Min, Yu Wang, Yupeng |
| author_facet | Gao, Hui Min, Yu Wang, Yupeng |
| contents | We systematically study relative and absolute $Δ_{\mathrm{dR}}^+$-crystals on the (log-) prismatic site of a smooth (resp.~ semi-stable) formal scheme. Using explicit computation of stratifications, we classify (local) relative crystals by certain nilpotent connections, and classify (local) absolute crystals by certain enhanced connections. By using a $p$-adic Riemann--Hilbert functor and an infinite dimensional Sen theory over the Kummer tower, we globalize the results on absolute crystals and further classify them by certain small (global) $\mathbb{B}_{\mathrm{dR}}^+$-local systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic crystals and $p$-adic Riemann--Hilbert correspondence Gao, Hui Min, Yu Wang, Yupeng Number Theory Algebraic Geometry We systematically study relative and absolute $Δ_{\mathrm{dR}}^+$-crystals on the (log-) prismatic site of a smooth (resp.~ semi-stable) formal scheme. Using explicit computation of stratifications, we classify (local) relative crystals by certain nilpotent connections, and classify (local) absolute crystals by certain enhanced connections. By using a $p$-adic Riemann--Hilbert functor and an infinite dimensional Sen theory over the Kummer tower, we globalize the results on absolute crystals and further classify them by certain small (global) $\mathbb{B}_{\mathrm{dR}}^+$-local systems. |
| title | Prismatic crystals and $p$-adic Riemann--Hilbert correspondence |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2411.18780 |