A stacky nilpotent $p$-adic Riemann-Hilbert correspondence
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909391394963456 |
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| author | Liu, Yudong Ma, Chenglong Nie, Xiecheng Qu, Xiaoyu |
| author_facet | Liu, Yudong Ma, Chenglong Nie, Xiecheng Qu, Xiaoyu |
| contents | Let $\overline X$ be a smooth rigid variety over $C=\mathbb C_p$ admitting a lift $X$ over $B_{dR}^+$. In this paper, we use the stacky language to prove a nilpotent $p$-adic Riemann-Hilbert correspondence. After introducing the moduli stack of $\mathbb B^+_{dR}$-local systems and $t$-connections, we prove that there is an equivalence of the nilpotent locus of the two stacks: $RH^0:LS^0_X \to tMIC^0_X$, where $LS^0_X$ is the stack of nilpotent $\mathbb B^+_{dR}$-local systems on $\overline X_{1,v}$ and $tMIC^0_X$ is the stack of $\mathcal{O}_X$-bundles with integrable $t$-connection on $X_{et}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stacky nilpotent $p$-adic Riemann-Hilbert correspondence Liu, Yudong Ma, Chenglong Nie, Xiecheng Qu, Xiaoyu Algebraic Geometry Number Theory Let $\overline X$ be a smooth rigid variety over $C=\mathbb C_p$ admitting a lift $X$ over $B_{dR}^+$. In this paper, we use the stacky language to prove a nilpotent $p$-adic Riemann-Hilbert correspondence. After introducing the moduli stack of $\mathbb B^+_{dR}$-local systems and $t$-connections, we prove that there is an equivalence of the nilpotent locus of the two stacks: $RH^0:LS^0_X \to tMIC^0_X$, where $LS^0_X$ is the stack of nilpotent $\mathbb B^+_{dR}$-local systems on $\overline X_{1,v}$ and $tMIC^0_X$ is the stack of $\mathcal{O}_X$-bundles with integrable $t$-connection on $X_{et}$. |
| title | A stacky nilpotent $p$-adic Riemann-Hilbert correspondence |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2411.10165 |